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Dissertations / Theses on the topic 'Nonabelian class field theory'

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Published: 4 June 2021

Last updated: 27 July 2025

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1

Abramov, Gueorgui. "Nilpotent Class Field Theory." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 1999. http://dx.doi.org/10.18452/14361.

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2

Mukai, Daichi. "Mirror symmetry of nonabelian Landau-Ginzburg orbifolds with loop type potentials." Kyoto University, 2020. http://hdl.handle.net/2433/253068.

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3

Mohamed, Adam. "Local Class Field Theory via Lubin-Tate Theory /." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/1936.

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4

Hofmann, Walter. "Class field theory for arithmetic schemes." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985500964.

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5

Rakotoniaina, Tahina. "Explicit class field theory for rational function fields." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/1993.

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6

Newton, Rachel Dominica. "Central simple algebras, cup-products and class field theory." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610730.

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7

Yoon, Seok Ho. "Explicit class field theory : one dimensional and higher dimensional." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/50367/.

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This thesis investigates class field theory for one dimensional fields and higher dimensional fields. For one dimensional fields we cover the cases of local fields and global fields of positive characteristic. For higher dimensional fields we study the case of higher local fields of positive characteristic. The main content of the thesis is divided into two parts. The first part solves several problems directly related to Neukirch's axiomatic class field theory method. We first prove the famous Hilbert 90 Theorem in the case of tamely ramified extensions of local fields in an explicit way. Thi

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8

Ellenburg, Michael Glen. "Massless particles in a class of field theories." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/28022.

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9

Syder, Kirsty. "Two-dimensional local-global class field theory in positive characteristic." Thesis, University of Nottingham, 2014. http://eprints.nottingham.ac.uk/14538/.

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Using the higher tame symbol and Kawada and Satake’s Witt vector method, A.N. Parshin developed class field theory for positive characteristic higher local fields, defining reciprocity maps separately for the tamely ramified and wildly ramified cases. We prove reciprocity laws for these symbols using techniques of Morrow for the Witt symbol and Romo for the higher tame symbol. We then extend this method of defining a reciprocity map to the case of positive characteristic local- global fields associated to points and curves on an algebraic surface over a finite field.

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10

Rozario, Rebecca. "The Distribution of the Irreducibles in an Algebraic Number Field." Fogler Library, University of Maine, 2003. http://www.library.umaine.edu/theses/pdf/RozarioR2003.pdf.

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11

Liu, Dunxue Carleton University Dissertation Mathematics. "Dihedral polynomial congruences and binary quadratic forms: a class field theory approach." Ottawa, 1992.

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12

Stigner, Carl. "Hopf and Frobenius algebras in conformal field theory." Doctoral thesis, Karlstads universitet, Avdelningen för fysik och elektroteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-14456.

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There are several reasons to be interested in conformal field theories in two dimensions. Apart from arising in various physical applications, ranging from statistical mechanics to string theory, conformal field theory is a class of quantum field theories that is interesting on its own. First of all there is a large amount of symmetries. In addition, many of the interesting theories satisfy a finiteness condition, that together with the symmetries allows for a fully non-perturbative treatment, and even for a complete solution in a mathematically rigorous manner. One of the crucial tools which

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13

McLeman, Cameron William. "A Golod-Shafarevich Equality and p-Tower Groups." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/194026.

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Let K be a quadratic imaginary number field, let Kp^(infinity) the top of its p-class field tower for p an odd prime, and let G=Gal(Kp^(infinity)/K). It is known, due to a tremendous collection of work ranging from the principal results of class field theory to the famous Golod-Shafarevich inequality, that G is finite if the p-rank of the class group of K is 0 or 1, and is infinite if this rank is at least 3. This leaves the rank 2 case as the only remaining unsolved case. In this case, while finiteness is still a mystery, much is still known about G: It is a 2-generated, 2-related pro-p-gr

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14

Rada, Ion Kolster Manfred. "The Lichtenbaum conjecture at the prime 2 /." *McMaster only, 2002.

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15

Sigl, Martin [Verfasser], and Alexander [Akademischer Betreuer] Schmidt. "Ramification filtration by moduli in higher-dimensional global class field theory / Martin Sigl ; Betreuer: Alexander Schmidt." Heidelberg : Universitätsbibliothek Heidelberg, 2013. http://d-nb.info/117714865X/34.

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16

Bembom, Tobias [Verfasser], Preda [Akademischer Betreuer] Mihăilescu, and Valentin [Akademischer Betreuer] Blomer. "The Capitulation Problem in Class Field Theory / Tobias Bembom. Gutachter: Preda Mihailescu ; Valentin Blomer. Betreuer: Preda Mihailescu." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2012. http://d-nb.info/1044046805/34.

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17

Laughlin, Anne Margaret. "Student Ratings of Instruction: Examining the Role of Academic Field, Course Level, and Class Size." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/47353.

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This dissertation investigated the relationship between course characteristics and student ratings of instruction at a large research intensive university. Specifically, it examined the extent to which academic field, course level, and class size were associated with variation in mean class ratings. Past research consistently identifies differences between student ratings in different academic fields, but offers no unifying conceptual framework for the definition or categorization of academic fields. Therefore, two different approaches to categorizing classes into academic fields were compar

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18

Reglade, Stephanie. "Différentes approches de la théorie l-adique du corps des classes." Thesis, Bordeaux, 2014. http://www.theses.fr/2014BORD0168/document.

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Neukirch a développé la théorie abstraite du corps des classes dans son livre ``Class Field Theory''. Nous montrons qu'il est possible de déduire la théorie l-adique de Jaulentdu travail de Neukirch. La preuve nécessite, dans les deux cas (le cas local et le cas global) de définir les applications degré, les G-modules, valuations convenables et de prouver l'axiome du corps des classes. } Puis nous montrons qu'en considérant le même objet local, mais cette fois-ci muni de la valuation logarithmique, et en remplaçant l'extension maximale non ramifiée du corps local considéré par la $\mathbb{Z}_{

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19

RIGATO, ALESSANDRA. "Uniqueness of optimal curves over F2 of small genus." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2009. http://hdl.handle.net/2108/1073.

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Una curva ottimale su Fq è definita come una curva proiettiva, liscia e assolutamente irriducibile definita sul campo finito Fq che ha il massimo numero di punti Fq-razionali consentito per il suo genere. I primi esempi di crve ottimali definite su F2 risalgono agli anni ottanta e sono dovuti a J.-P.Serre: applicando tecniche di teoria del corpo delle classi, Serre costruisce queste curve come ricoprimenti abeliani della retta proiettiva o di una curva ellittica di equazione data definita su F2. Dimostriamo in questa tesi che una curva ottimale di genere g definita su F2 è unica a meno di F2-m

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20

Milovic, Djordjo. "On the 16-rank of class groups of quadratic number fields." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS157/document.

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Nous démontrons deux nouveaux résultats de densité à propos du 16-rang des groupes des classes de corps de nombres quadratiques. Le premier des deux est que le groupe des classes de Q(sqrt{-p}) a un élément d'ordre 16 pour un quart des nombres premiers p qui sont de la forme a^2+c^4 avec c pair. Le deuxième est que le groupe des classes de Q(sqrt{-2p}) a un élément d'ordre 16 pour un huitième des nombres premiers p=-1 (mod 4). Ces résultats de densité sont intéressants pour plusieurs raisons. D'abord, ils sont les premiers résultats non triviaux de densité sur le 16-rang des groupes des classe

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21

Longino, Brando. "Exact S-matrices for a class of 1+1-dimensional integrable factorized scattering theories with Uq(sl2) symmetry and arbitrary spins." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20542/.

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In this thesis we will study the S-matrices associated to a new class of (1+1)-dimensional integrable models with Uq(sl2) symmetry, whose asymptotic particle states organize into a k/2 isospin multiplet, with k= 0,1,2,... Such S-matrices generalize the case study previously analyzed by S. R. Aladim and M. J. Martins, where it was only investigated the non-deformed limit q→1 of pure SU(2) symmetry. We check that the proposed S-matrix satisfies the constraints due to the the Yang-Baxter equation, crossing-symmetry requirement and unitarity and therefore defines a self-consistent integrable fact

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22

Barrientos, Ivan [Verfasser], and Moritz [Akademischer Betreuer] Kerz. "Wild ramification of schemes via curves, the rank 1 case (with applications to higher class field theory) / Ivan Barrientos. Betreuer: Moritz Kerz." Regensburg : Universitätsbibliothek Regensburg, 2014. http://d-nb.info/1058477455/34.

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23

Acosta-Jara. "Alguns problemas da radiação síncrotron /." São Paulo, 2002. http://hdl.handle.net/11449/132806.

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Orientador: Dmitri Maximovitch Gitman<br>Banca: Abraham Hirsz Zimerman<br>Banca: Jeferson de Lima Tomazelli<br>Banca: Antonio Edson Gonçalves<br>Banca: Bruto Max Pimentel Escobar<br>Resumo: Estudamos a radiação síncrotron (RS) de uma partícula carregada em um campo magnético uniforme e constante com influência do solenóide de Aharonov-Bohm dentro do quadro da teoria quântica relativística. Usando as soluções de Klein-Gordon são calculadas e analisadas as características da radiação espontânea de um fóton, tais como a intensidade, a distribuição angular e a polarização. É também apresentado uma

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24

Byard, Kevin. "Qualified difference sets : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand." Massey University, 2009. http://hdl.handle.net/10179/1204.

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Qualified difference sets are a class of combinatorial configuration. The sets are related to the residue difference sets that were first discussed in detail in 1953 by Emma Lehmer. Qualified difference sets consist of a set of residues modulo an integer v and they possess attractive properties that suggest potential applications in areas such as image formation, signal processing and aperture synthesis. This thesis outlines the theory behind qualified difference sets and gives conditions for the existence and nonexistence of these sets in various cases. A special case of the qualified differe

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25

Emmelin, Etienne. "Grοupes de classes et de Ροlya d'extensiοns abéliennes". Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMC241.

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Pour des extensions galoisiennes K/Q, le groupe de Pólya de K est un sous-groupedu groupe de classes d’idéaux de K engendré par les idéaux ambiges. On démontredans cette thèse l’existence d’une infinité d’extensions abéliennes K/Q, dont le groupede Pólya est isomorphe à un groupe abélien fini G, prescrit. Pour cela on se ramèneau cas des l-extensions cycliques et l’on utilise le théorème de structure des groupesabéliens finis. De plus, on étudie le comportement asymptotique du groupe de classesrelatif d’extensions CM abéliennes K/Q, défini comme étant le quotient du groupede classes Cl(K), par

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26

Cobbe, Alessandro. "Steinitz classes of tamely rami ed Galois extensions of algebraic number fields." Doctoral thesis, Scuola Normale Superiore, 2009. http://hdl.handle.net/11384/85661.

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27

Ferreira, Luan Alberto. "Teoria de corpos de classe e aplicações." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-05122012-102820/.

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Neste projeto, propomos estudar a chamada \"Teoria de Corpos de Classe,\" que oferece uma descrição simples das extensões abelianas de corpos locais e globais, bem como algumas de suas aplicações, como os teoremas de Kronecker-Weber e Scholz-Reichardt<br>In this work, we study the so called \"Class Field Theory\", which give us a simple description of the abelian extension of local and global elds. We also study some applications, like the Kronecker-Weber and Scholz-Reichardt theorems

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28

Viguié, Stéphane. "Contribution à l’étude de la conjecture de Gras et de la conjecture principale d’Iwasawa, par les systèmes d’Euler." Thesis, Besançon, 2011. http://www.theses.fr/2011BESA2026/document.

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Le but de ce travail est de montrer comment la théorie des systèmes d’Euler permet de comparer, dans certaines extensions abéliennes, le module galoisien des unités globales modulo unités de Stark avec le module galoisien des p-classes d’idéaux. On ne s’intéresse ici qu’aux extensions abéliennes ayant pour corps de base k un corps quadratique imaginaire, ou un corps global de caractéristique non nulle. La conjecture de Gras prévoit que pour toute extension abélienne finie K/k, tout nombre premier p premier à [K : k], et tout Qp-caractère ψ irréductible et non trivial de Gal (K/k), les ψ-partie

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29

Angelakis, Athanasios. "Universal Adelic Groups for Imaginary Quadratic Number Fields and Elliptic Curves." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0180/document.

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Cette thèse traite de deux problèmes dont le lien n’est pas apparent (1) A` quoi ressemble l’abélianisé AK du groupe de Galois absolu d’un corps quadratique imaginaire K, comme groupe topologique? (2) A` quoi ressemble le groupe des points adéliques d’une courbe elliptique sur Q, comme groupe topologique? Pour la première question, la restriction au groupe de Galois abélianisé nous permet d’utiliser la théorie du corps de classes pour analyser AK . Les travaux précédents dans ce domaine, qui remontent à Kubota et Onabe, décrivent le dual de Pontryagin de AK en termes de familles in- finies d’i

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30

Villanueva, Gutiérrez José Ibrahim. "Sur quelques questions en théorie d'Iwasawa." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0637/document.

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Ce travail de thèse comporte l'étude des invariants logarithmiques le long des $l^{d}$-extensions et se compose de trois parties étroitement reliées. La première partie est un compendium sur les divers approches à l'arithmétique algorithmique, c'est à dire l'étude générale des invariants logarithmiques. En particulier on y présente quatre définitions équivalentes du groupe de classes logarithmiques et on y démontre leur équivalence. On donne aussi une preuve alternative d'un théorème d'Iwasawa de type logarithmique. La deuxième partie s'interprète comme un addendum historique sur l'étude du gr

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31

García-Zelada, David. "Aspects géométriques et probabilistes des gaz de coulomb Concentration for Coulomb gases on compact manifolds A large deviation principle for empirical measures on Polish spaces: Application to singular Gibbs measures on manifolds Extremal particles of two-dimensional Coulomb gases and random polynomials on a positive background Edge fluctuations for a class of two-dimensional determinantal Coulomb gases." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLED046.

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Nous explorons des modèles probabilistes appelés gaz de Coulomb. Ils apparaissent dans différents contextes comme par exemple dans la théorie des matrices aléatoires, l'effet Hall quantique fractionnaire de Laughlin et les modèles de supraconductivité de Ginzburg-Landau. Dans le but de mieux comprendre le rôle de l'espace ambiant, nous étudions des versions géométriques de ce système. Nous exploitons trois structures sur ce modèle. La première est définie par la interaction électrostatique provenant de la loi de Gauss. La deuxième est la structure déterminantale disponible que pour des valeurs

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32

Blondeau, Julien. "Déformation des extensions peu ramifiées en P." Phd thesis, Université de Franche-Comté, 2011. http://tel.archives-ouvertes.fr/tel-00936135.

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33

Ducet, Virgile. "Construction of algebraic curves with many rational points over finite fields." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4043/document.

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L'étude du nombre de points rationnels d'une courbe définie sur un corps fini se divise naturellement en deux cas : lorsque le genre est petit (typiquement g<=50), et lorsqu'il tend vers l'infini. Nous consacrons une partie de cette thèse à chacun de ces cas. Dans la première partie de notre étude nous expliquons comment calculer l'équation de n'importe quel revêtement abélien d'une courbe définie sur un corps fini. Nous utilisons pour cela la théorie explicite du corps de classe fournie par les extensions de Kummer et d'Artin-Schreier-Witt. Nous détaillons également un algorithme pour la r

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34

Bembom, Tobias. "The Capitulation Problem in Class Field Theory." Doctoral thesis, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F05F-8.

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35

Abramov, Gueorgui [Verfasser]. "Nilpotent class field theory / von Gueorgui Abramov." 1999. http://d-nb.info/956434495/34.

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36

莊子平. "Explicit Class Field Theory for Kummer Extensions." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/685d2x.

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碩士<br>國立臺灣師範大學<br>數學系<br>96<br>In this thesis, we first introduce some known results. Then we define a pairing and use the known results to discuss properties of this pairing. Finally, we use this pairing to discuss local class field theory for Kummer extension without employing the classical local class field theory.

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37

"Local class field theory via group cohomology method." Chinese University of Hong Kong, 1996. http://library.cuhk.edu.hk/record=b5888933.

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by Au Pat Nien.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.<br>Includes bibliographical references (leaves 86-88).<br>Chapter 1 --- Introduction --- p.1<br>Chapter 2 --- Valuations --- p.4<br>Chapter 2.1 --- Preliminaries --- p.4<br>Chapter 2.2 --- Complete Fields --- p.6<br>Chapter 2.3 --- Unramified Extension of Complete Field --- p.10<br>Chapter 2.4 --- Local Fields --- p.12<br>Chapter 3 --- Ramification Groups and Hasse-Herbrand Function --- p.16<br>Chapter 3.1 --- Ramification Groups --- p.16<br>Chapter 3.2 --- "The Quotients Gi/Gi+1, i ≥ 0" --- p.17<br>Chapter 3.

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38

Cheng, Derek. "Drinfeld modules, Explicit class field theory and Lambda-structures." Phd thesis, 2022. http://hdl.handle.net/1885/270084.

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This thesis translates some $\Lambda$-geometric results from number fields, to function fields. There are two major results in this thesis. For each set $P$ of almost all primes of $\fp[t]$, we use $R_P$ to denote the ring corresponding to an affine open subsets of $\mathbb{P}^1_{\fp}$, i.e., the closed points of $R_P$ are the elements in $P$. We give an equivalent condition for a finite \'{e}tale $\Lambda$-scheme $S$ over $\mbox{Spec}(\fp(t))$ to have a $Q$-$\Lambda(P)$-model, by which we mean a finite flat and reduced scheme over $\mbox{Spec}(R_Q)$ together with a family of commuting

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39

Hofmann, Walter [Verfasser]. "Class field theory for arithmetic schemes / vorgelegt von Walter Hofmann." 2007. http://d-nb.info/985500964/34.

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40

"Survey on Birch and Swinnerton-Dyer conjecture." Chinese University of Hong Kong, 1992. http://library.cuhk.edu.hk/record=b5887034.

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by Leung Tak.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1992.<br>Includes bibliographical references (leaves 76-77).<br>Chapter 1 --- Introduction --- p.1<br>Chapter 2 --- Elliptic curve --- p.4<br>Chapter 2.1 --- Elliptic Curve in Normal Form --- p.4<br>Chapter 2.2 --- Geometry and Group Law --- p.7<br>Chapter 2.3 --- Special Class of Elliptic Curves --- p.10<br>Chapter 2.4 --- Mordell's Conjecture --- p.12<br>Chapter 2.5 --- Torsion Group --- p.14<br>Chapter 2.6 --- Selmer Group and Tate-Shafarevitch. Group --- p.16<br>Chapter 2.7 --- Endomorphism of Elliptic Curves ---

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41

Persad, Ishwar. "Seeking a Kaleidoscopic Lens: A Holistic Analysis of the Psychedelic Field." Thesis, 2010. http://hdl.handle.net/1807/24618.

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The psychedelic field has generated a vast body of work in terms of psychology, art, spirituality and understandings of the mind and consciousness. Having engaged with the field for the last ten years, I have been curious as to why issues of race, gender and class are not included in the analysis and theories that are generated from the field. My background in feminism, queer studies, anti-racism, critical theory and social justice, as well as my interest in consciousness and psychedelics, led me to conduct a literature review and analyze it with a critical framework. The literature showed an

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42

Hopkins, Kimberly Michele. "Periods of modular forms and central values of L-functions." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-05-1423.

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This thesis is comprised of three problems in number theory. The introduction is Chapter 1. The first problem is to partially generalize the main theorem of Gross, Kohnen and Zagier to higher weight modular forms. In Chapter 2, we present two conjectures which do this and some partial results towards their proofs as well as numerical examples. This work provides a new method to compute coefficients of weight k+1/2 modular forms for k>1 and to compute the square roots of central values of L-functions of weight 2k>2 modular forms. Chapter 3 presents four different interpretations of the m

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