Relevant bibliographies by topics / Iwasawa algebras

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Iwasawa algebras'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Iwasawa algebras"

1

Johnston, Henri, and Andreas Nickel. "Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture." American Journal of Mathematics 140, no. 1 (2018): 245–76. http://dx.doi.org/10.1353/ajm.2018.0005.

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Ardakov, K., F. Wei, and J. J. Zhang. "Reflexive ideals in Iwasawa algebras." Advances in Mathematics 218, no. 3 (2008): 865–901. http://dx.doi.org/10.1016/j.aim.2008.02.004.

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Ardakov, Konstantin. "Krull dimension of Iwasawa algebras." Journal of Algebra 280, no. 1 (2004): 190–206. http://dx.doi.org/10.1016/j.jalgebra.2004.06.014.

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Han, Dong, та Feng Wei. "Normal elements in the mod-𝑝 Iwasawa algebra over SL𝑛(ℤ𝑝): A computational approach". Forum Mathematicum 31, № 6 (2019): 1417–46. http://dx.doi.org/10.1515/forum-2018-0260.

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AbstractThis is the last in a series of articles where we are concerned with normal elements of noncommutative Iwasawa algebras over {\mathrm{SL}_{n}(\mathbb{Z}_{p})}. Our goal in this portion is to give a positive answer to an open question in [D. Han and F. Wei, Normal elements of noncommutative Iwasawa algebras over \mathrm{SL}_{3}(\mathbb{Z}_{p}), Forum Math. 31 2019, 1, 111–147] and make up for an earlier mistake in [F. Wei and D. Bian, Normal elements of completed group algebras over \mathrm{SL}_{n}(\mathbb{Z}_{p}), Internat. J. Algebra Comput. 20 2010, 8, 1021–1039] simultaneously. Let
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ARDAKOV, KONSTANTIN. "Prime ideals in noncommutative Iwasawa algebras." Mathematical Proceedings of the Cambridge Philosophical Society 141, no. 02 (2006): 197. http://dx.doi.org/10.1017/s030500410600939x.

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Ardakov, K., та S. J. Wadsley. "Γ-invariant ideals in Iwasawa algebras". Journal of Pure and Applied Algebra 213, № 9 (2009): 1852–64. http://dx.doi.org/10.1016/j.jpaa.2009.02.001.

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Wei, Feng. "Homological properties of noncommutative Iwasawa algebras." Comptes Rendus Mathematique 349, no. 1-2 (2011): 15–20. http://dx.doi.org/10.1016/j.crma.2010.11.030.

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Ardakov, Konstantin. "Prime ideals in nilpotent Iwasawa algebras." Inventiones mathematicae 190, no. 2 (2012): 439–503. http://dx.doi.org/10.1007/s00222-012-0385-4.

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Barnes, Donald W. "Ado-Iwasawa extras." Journal of the Australian Mathematical Society 78, no. 3 (2005): 407–21. http://dx.doi.org/10.1017/s1446788700008600.

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AbstractLet L be a finite-dimensional Lie algebra over the field F. The Ado-Iwasawa Theorem asserts the existence of a finite-dimensional L-module which gives a faithful representation ρ of L. Let S be a subnormal subalgebra of L, let be a saturated formation of soluble Lie algebras and suppose that S ∈ . I show that there exists a module V with the extra property that it is -hypercentral as S-module. Further, there exists a module V which has this extra property simultaneously for every such S and , along with the Hochschild extra that ρ(x) is nilpotent for every x ∈ L with ad(x) nilpotent. I
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ARDAKOV, KONSTANTIN. "LOCALISATION AT AUGMENTATION IDEALS IN IWASAWA ALGEBRAS." Glasgow Mathematical Journal 48, no. 02 (2006): 251. http://dx.doi.org/10.1017/s0017089506003041.

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Dissertations / Theses on the topic "Iwasawa algebras"

1

Ardakov, Konstantin. "Krull dimension of Iwasawa algebras and some related topics." Thesis, University of Cambridge, 2004. https://www.repository.cam.ac.uk/handle/1810/251918.

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Ray, Jishnu. "Iwasawa algebras for p-adic Lie groups and Galois groups." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS189/document.

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Un outil clé dans la théorie des représentations p-adiques est l'algèbre d'Iwasawa, construit par Iwasawa pour étudier les nombres de classes d'une tour de corps de nombres. Pour un nombre premier p, l'algèbre d'Iwasawa d'un groupe de Lie p-adique G, est l'algèbre de groupe G complétée non-commutative. C'est aussi l'algèbre des mesures p-adiques sur G. Les objets provenant de groupes semi-simples, simplement connectés ont des présentations explicites comme la présentation par Serre des algèbres semi-simples et la présentation de groupe de Chevalley par Steinberg. Dans la partie I, nous donnons
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Zähringer, Yasin Hisam Julian. "Non-commutative Iwasawa theory with (φ,Γ)-local conditions over distribution algebras". Thesis, King's College London (University of London), 2017. https://kclpure.kcl.ac.uk/portal/en/theses/noncommutative-iwasawa-theory-with-local-conditions-over-distribution-algebras(77477392-e3b4-4eb1-8acc-e59789517360).html.

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In this thesis we formulate a natural non-commutative Iwasawa Main Conjecture for motives which fulfil the Dabrowski-Panchishkin condition on the level of (φ,Γ)-modules. The basic framework we employ is still Fukaya-Kato’s but we work systematically over Schneider-Teitelbaum’s distribution algebras of compact p-adic Lie groups instead of Iwasawa algebras. This allows us to consider as local conditions not just subrepresentations of the p-adic realisation which fulfil the Dabrowski-Panchishkin conditions but also sub-(φ,Γ)-modules which fulfil the analogous Dabrowski-Panchishkin conditions. We
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Buyukboduk, Kazim. "Kolyvagin Systems over an Iwasawa algebra /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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Solanki, Vishal. "Whitehead group of the Iwasawa algebra of GL2(Zp)." Thesis, King's College London (University of London), 2018. https://kclpure.kcl.ac.uk/portal/en/theses/whitehead-group-of-the-iwasawa-algebra-of-gl2zp(d1cd25d8-c5dd-4365-8a4d-f384b4c08b11).html.

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Main conjectures in Iwasawa theory are interesting because they give a deep connection between arithmetic and analytic objects in number theory. One of the most important recent developments in Iwasawa theory is the formulation of non-commutative main conjectures by Coates, Fukaya, Kato, Sujatha and Venjakob using K1 groups. Burns and Kato supplied a strategy to prove these non-commutative main conjectures. After important special cases were proved by Kato and Hara, the non-commutative main conjecture for totally real fields was proved by Kakde using this strategy (it was proved independently
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Drinen, Michael Jeffrey. "Iwasawa mu-invariants of Selmer groups /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5810.

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Minardi, John. "Iwasawa modules for [p-adic]-extensions of algebraic number fields /." Thesis, Connect to this title online; UW restricted, 1986. http://hdl.handle.net/1773/5742.

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Ponsinet, Gautier. "On the algebraic side of the Iwasawa theory of some non-ordinary Galois representations." Doctoral thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/32466.

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Soit F un corps de nombres non-ramifié en un nombre premier impair p. Soit F∞) la Zp-extension cyclotomique de F et Λ = Zp [[Gal(F∞ /F)]] l’algèbre d’Iwasawa de Gal (F∞ /F) (signe de asymptotiquement égal) Zp sur Zp. Généralisant les groupes de Selmer plus et moins de Kobayashi, Büyükboduk et Lei ont défini des groupes de Selmer signés sur F∞ pour certaines représentations galoisiennes. En particulier, leurs constructions s’appliquent aux cas des variétés abéliennes définies sur F ayant bonne réduction supersingulière en chaque premier de F divisant p. Ces groupes de Selmer signés ont naturell
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Baccari, Kevin J. "Homomorphic Images And Related Topics." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/224.

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We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m*n and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2*n: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M11 and M11, as well as some classical groups. We wil
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Lamp, Leonard B. "SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/222.

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The goal of this thesis is to show constructions of some of the sporadic groups such as the Mathieu group, M12, J1, Projective Special Linear groups, PSL(2,8), and PSL(2,11), Unitary group U(3,3) and many other non-abelian simple groups. Our purpose is to find all simple non-abelian groups as homomorphic images of permutation or monomial progenitors, as well grasping a deep understanding of group theory and extension theory to determine groups up to isomorphisms. The progenitor, developed by Robert T. Curtis, is a semi-direct product of the following form: P≅2*n: N = {πw | π ∈ N, w a reduced w
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Books on the topic "Iwasawa algebras"

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Ritter, J. The lifted root number conjecture and Iwasawa theory. American Mathematical Society, 2002.

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1927-, Satake Ichirō, ed. Kenkichi Iwasawa collected papers. Springer, 2001.

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Iwasawa, Kenkichi. Kenkichi Iwasawa collected papers. Springer, 2001.

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Hilbert modular forms and Iwasawa theory. Clarendon, 2006.

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1958-, Childress Nancy, and Jones John W. 1961-, eds. Arithmetic geometry: Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993, Arizona State University. American Mathematical Society, 1994.

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Perrin-Riou, Bernadette. Théorie d'Iwasawa des représentations p-adiques semi-stables. Société Mathématique de France, 2001.

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Perrin-Riou, Bernadette. Théorie d'Iwasawa des représentations p-adiques semi-stables. Société Mathématique de France, 2001.

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Weiss, Alfred. The Lifted Root Number Conjecture and Iwasawa Theory. American Mathematical Society, 2002.

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9

(Editor), Genjiro Fujisaki, Kato Kazuya (Editor), Masato Kurihara (Editor), Shoichi Nakajima (Editor), and Ichiro Satake (Editor), eds. Kenkichi Iwasawa Collected Papers: Volume 1, 2. Springer, 2001.

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10

J, Coates, and Iwasawa Kenkichi 1917-, eds. Algebraic number theory: In honor of K. Iwasawa. Academic Press, 1989.

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Book chapters on the topic "Iwasawa algebras"

1

Satake, Ichiro, Genjiro Fujisaki, Kazuya Kato, Masato Kurihara, and Shoichi Nakajima. "On the representation of Lie algebras." In Kenkichi Iwasawa Collected Papers. Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67947-9_16.

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Schneider, Peter, and Otmar Venjakob. "K 1 of Certain Iwasawa Algebras, After Kakde." In Noncommutative Iwasawa Main Conjectures over Totally Real Fields. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32199-3_4.

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Satake, Ichiro, Genjiro Fujisaki, Kazuya Kato, Masato Kurihara, and Shoichi Nakajima. "On Г-extensions of algebraic number fields." In Kenkichi Iwasawa Collected Papers. Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67947-9_35.

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Satake, Ichiro, Genjiro Fujisaki, Kazuya Kato, Masato Kurihara, and Shoichi Nakajima. "On Zℓ-extensions of algebraic number fields." In Kenkichi Iwasawa Collected Papers. Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67947-9_52.

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Greenberg, Ralph. "Introduction to Iwasawa theory for elliptic curves." In Arithmetic Algebraic Geometry. American Mathematical Society, 2008. http://dx.doi.org/10.1090/pcms/009/06.

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Satake, Ichiro, Genjiro Fujisaki, Kazuya Kato, Masato Kurihara, and Shoichi Nakajima. "A note on class numbers of algebraic number fields." In Kenkichi Iwasawa Collected Papers. Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67947-9_32.

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Satake, Ichiro, Genjiro Fujisaki, Kazuya Kato, Masato Kurihara, and Shoichi Nakajima. "On some infinite Abelian extensions of algebraic number fields." In Kenkichi Iwasawa Collected Papers. Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67947-9_49.

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Satake, Ichiro, Genjiro Fujisaki, Kazuya Kato, Masato Kurihara, and Shoichi Nakajima. "On a certain analogy between algebraic number fields and function fields." In Kenkichi Iwasawa Collected Papers. Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67947-9_40.

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Satake, Ichiro, Genjiro Fujisaki, Kazuya Kato, Masato Kurihara, and Shoichi Nakajima. "A note on the group of units of an algebraic number field." In Kenkichi Iwasawa Collected Papers. Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67947-9_31.

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Mitchell, Stephen A. "K(1)-Local Homotopy, Iwasawa Theory and Algebraic K-Theory." In Handbook of K-Theory. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-27855-9_19.

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