Relevant bibliographies by topics / Finite fields (Algebra) Geometry, Projective

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Academic literature on the topic 'Finite fields (Algebra) Geometry, Projective'

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Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Finite fields (Algebra) Geometry, Projective"

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RAFIE-RAD, M. "SPECIAL PROJECTIVE ALGEBRA OF RANDERS METRICS OF CONSTANT S-CURVATURE." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1250034. http://dx.doi.org/10.1142/s021988781250034x.

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The collection of all projective vector fields on a Finsler space (M, F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra. A specific Lie sub-algebra of projective algebra of Randers spaces (called the special projective algebra) of non-zero constant S-curvature is studied and it is proved that its dimension is at most [Formula: see text]. Moreover, a local characterization of Randers spaces whose special projective algebra has maximum dimension is established. The results uncover somehow the complexity of projective Finsler geometry versus Riemannian geometry.
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González-Avilés, Cristian D. "On K2 of varieties over number fields." Journal of K-Theory 1, no. 1 (January 7, 2008): 175–83. http://dx.doi.org/10.1017/is007011012jkt004.

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AbstractLet k be a number field and let X be a smooth, projective and geometrically integral k-variety. We show that, if the geometric Néron-Severi group of X is torsion-free, then the Galois cohomology group is finite. Previously this group was only known to have a finite exponent. We also obtain a vanishing theorem for this group, showing in particular that it is trivial if X belongs to a certain class of abelian varieties with complex multiplication. The interest in the above cohomology group stems from its connection to the torsion subgroup of the Chow group CH2(X) of codimension 2 cycles on X. In the last section of the paper we record certain results on curves which must be familiar to all specialists in this area but which we have not formerly seen in print.
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Miyatani, Kazuaki, and Makoto Sano. "An exponential sum and higher-codimensional subvarieties of projective spaces over finite fields." Hiroshima Mathematical Journal 44, no. 3 (November 2014): 327–40. http://dx.doi.org/10.32917/hmj/1419619750.

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Antieau, Benjamin, and Ben Williams. "Godeaux–Serre varieties and the étale index." Journal of K-Theory 11, no. 2 (April 2013): 283–95. http://dx.doi.org/10.1017/is013003003jkt220.

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AbstractWe use Godeaux–Serre varieties of finite groups, projective representation theory, the twisted Atiyah–Segal completion theorem, and our previous work on the topological period-index problem to compute the étale index of Brauer classes α ∈ Brét(X) in some specific examples. In particular, these computations show that the étale index of α differs from the period of α in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Godeaux–Serre varieties in terms of projective representation theory.
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Hu, Wenchuan. "On Additive invariants of actions of additive and multiplicative groups." Journal of K-theory 12, no. 3 (May 1, 2013): 551–68. http://dx.doi.org/10.1017/is013003003jkt219.

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AbstractLet X be an algebraic variety with an action of either the additive or multiplicative group. We calculate the additive invariants of X in terms of the additive invariants of the fixed point set, using a formula of Białynicki-Birula. The method is also generalized to calculate certain additive invariants for Chow varieties. As applications, we obtain results on the Hodge polynomial of Chow varieties in characteristic zero and the number of points for Chow varieties over finite fields. As applications, we obtain the l-adic Euler-Poincaré characteristic for the Chow varieties of certain projective varieties over a field of arbitrary characteristic. Moreover, we show that the virtual Hodge (p,0) and (0,q)-numbers of the Chow varieties and affine algebraic group varieties are zero for all p,q positive.
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Stebletsova, Vera, and Yde Venema. "Undecidable theories of Lyndon algebras." Journal of Symbolic Logic 66, no. 1 (March 2001): 207–24. http://dx.doi.org/10.2307/2694918.

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AbstractWith each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski's axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class L(G) of Lyndon algebras associated with projective geometries in G has an undecidable equational theory. In our proof we develop and use a connection between projective geometries and diagonal-free cylindric algebras.
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Shangdi, Chen, Zhang Xiaollian, and Ma Hao. "Two constructions of A3-codes from projective geometry in finite fields." Journal of China Universities of Posts and Telecommunications 22, no. 2 (April 2015): 52–59. http://dx.doi.org/10.1016/s1005-8885(15)60639-2.

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Wildberger, Norman. "Universal Hyperbolic Geometry, Sydpoints and Finite Fields: A Projective and Algebraic Alternative." Universe 4, no. 1 (January 1, 2018): 3. http://dx.doi.org/10.3390/universe4010003.

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Chen, Shangdi, and Xiaolian Zhang. "Three constructions of perfect authentication codes from projective geometry over finite fields." Applied Mathematics and Computation 253 (February 2015): 308–17. http://dx.doi.org/10.1016/j.amc.2014.12.088.

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Larose, Benoit. "Finite projective ordered sets." Order 8, no. 1 (1991): 33–40. http://dx.doi.org/10.1007/bf00385812.

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Dissertations / Theses on the topic "Finite fields (Algebra) Geometry, Projective"

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Culbert, Craig W. "Spreads of three-dimensional and five-dimensional finite projective geometries." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 101 p, 2009. http://proquest.umi.com/pqdweb?did=1891555371&sid=3&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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Grout, Jason Nicholas. "The Minimum Rank Problem Over Finite Fields." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1995.pdf.

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Giuzzi, Luca. "Hermitian varieties over finite fields." Thesis, University of Sussex, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326913.

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Caullery, Florian. "Polynomes sur les corps finis pour la cryptographie." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4013/document.

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Les fonctions de F_q dans lui-même sont des objets étudiés dans de divers domaines tels que la cryptographie, la théorie des codes correcteurs d'erreurs, la géométrie finie ainsi que la géométrie algébrique. Il est bien connu que ces fonctions sont en correspondance exacte avec les polynômes en une variable à coefficients dans F_q. Nous étudierons trois classes de polynômes particulières: les polynômes Presque Parfaitement Non linéaires (Almost Perfect Nonlinear (APN)), les polynômes planaires ou parfaitement non linéaire (PN) et les o-polynômes.Les fonctions APN sont principalement étudiées pour leurs applications en cryptographie. En effet, ces fonctions sont celles qui offre la meilleure résistance contre la cryptanalyse différentielle.Les polynômes PN et les o-polynômes sont eux liés à des problèmes célèbres de géométrie finie. Les premiers décrivent des plans projectifs et les seconds sont en correspondance directe avec les ovales et hyperovales de P^2(F_q). Néanmoins, leurs champ d'application a été récemment étendu à la cryptographie symétrique et à la théorie des codes correcteurs d'erreurs.L'un des moyens utilisé pour compléter la classification est de considérer les polynômes présentant l'une des propriétés recherchées sur une infinité d'extension de F_q. Ces fonctions sont appelées fonction APN (respectivement PN ou o-polynômes) exceptionnelles.Nous étendrons la classification des polynômes APN et PN exceptionnels et nous donneront une description complète des o-polynômes exceptionnels. Les techniques employées sont basées principalement sur la borne de Lang-Weil et sur des méthodes élémentaires
Functions from F_q to itself are interesting objects arising in various domains such as cryptography, coding theory, finite geometry or algebraic geometry. It is well known that these functions admit a univariate polynomial representation. There exists many interesting classes of such polynomials with plenty of applications in pure or applied maths. We are interested in three of them: Almost Perfect Nonlinear (APN) polynomials, Planar (PN) polynomials and o-polynomials. APN polynomials are mostly used in cryptography to provide S-boxes with the best resistance to differential cryptanalysis and in coding theory to construct double error-correcting codes. PN polynomials and o-polynomials first appeared in finite geometry. They give rise respectively to projective planes and ovals in P^2(F_q). Also, their field of applications was recently extended to symmetric cryptography and error-correcting codes.A complete classification of APN, PN and o-polynomials is an interesting open problem that has been widely studied by many authors. A first approach toward the classification was to consider only power functions and the studies were recently extended to polynomial functions.One way to face the problem of the classification is to consider the polynomials that are APN, PN or o-polynomials over infinitely many extensions of F_q, namely, the exceptional APN, PN or o-polynomials.We improve the partial classification of exceptional APN and PN polynomials and give a full classification of exceptional o-polynomials. The proof technique is based on the Lang-Weil bound for the number of rational points in algebraic varieties together with elementary methods
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Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions of covering curves: covers by the Hemitian curve, Kummer extensions and Artin-Schreier extensions. With these articles the great difficulty of finding explicit equations for curves with many rational points is overcome. With the method given by Arnaldo García in [6] we have been able to nd examples that can be used to define the lower bounds for the corresponding entries in the tables given in http: //wins.uva.nl/~geer, which to the time of writing this Thesis appear as "no information available". In fact, as the curves found are maximal, these entries no longer need a bound, they can be given by a unique entry, since the exact value of Nq(g) is now known.

At the end of the thesis an outline of the construction of Goppa codes is given and the NXL and XNL codes are presented.

 

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Hart, Derrick. "Explorations of geometric combinatorics in vector spaces over finite fields." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5585.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2008.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 8, 2009) Vita. Includes bibliographical references.
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Jogia, Danesh Michael Mathematics &amp Statistics Faculty of Science UNSW. "Algebraic aspects of integrability and reversibility in maps." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/40947.

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We study the cause of the signature over finite fields of integrability in two dimensional discrete dynamical systems by using theory from algebraic geometry. In particular the theory of elliptic curves is used to prove the major result of the thesis: that all birational maps that preserve an elliptic curve necessarily act on that elliptic curve as addition under the associated group law. Our result generalises special cases previously given in the literature. We apply this theorem to the specific cases when the ground fields are finite fields of prime order and the function field $mathbb{C}(t)$. In the former case, this yields an explanation of the aforementioned signature over finite fields of integrability. In the latter case we arrive at an analogue of the Arnol'd-Liouville theorem. Other results that are related to this approach to integrability are also proven and their consequences considered in examples. Of particular importance are two separate items: (i) we define a generalization of integrability called mixing and examine its relation to integrability; and (ii) we use the concept of rotation number to study differences and similarities between birational integrable maps that preserve the same foliation. The final chapter is given over to considering the existence of the signature of reversibility in higher (three and four) dimensional maps. A conjecture regarding the distribution of periodic orbits generated by such maps when considered over finite fields is given along with numerical evidence to support the conjecture.
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Castilho, Tiago Nunes 1983. "Sobre o numero de pontos racionais de curvas sobre corpos finitos." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307074.

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Orientador: Fernando Eduardo Torres Orihuela
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-10T15:12:25Z (GMT). No. of bitstreams: 1 Castilho_TiagoNunes_M.pdf: 813127 bytes, checksum: 313e9951b003dcd0e0876813659d7050 (MD5) Previous issue date: 2008
Resumo: Nesta dissertacao estudamos cotas para o numero de pontos racionais de curvas definidas sobre corpos finitos tendo como ponto de partida a teoria de Stohr-Voloch
Abstract: In this work we study upper bounds on the number of rational points of curves over finite fields by using the Stohr-Voloch theory
Mestrado
Algebra Comutativa, Geometria Algebrica
Mestre em Matemática
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Amorós, Carafí Laia. "Images of Galois representations and p-adic models of Shimura curves." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/471452.

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The Langlands program is a vast and unifying network of conjectures that connect the world of automorphic representations of reductive algebraic groups and the world of Galois representations. These conjectures associate an automorphic representation of a reductive algebraic group to every n-dimensional representation of a Galois group, and the other way around: they attach a Galois representation to any automorphic representation of a reductive algebraic group. Moreover, these correspondences are done in such a way that the automorphic L-functions attached to the two objects coincide. The theory of modular forms is a field of complex analysis whose main importance lies on its connections and applications to number theory. We will make use, on the one hand, of the arithmetic properties of modular forms to study certain Galois representations and their number theoretic meaning. On the other hand, we will use the geometric meaning of these complex analytic functions to study a natural generalization of modular curves. A modular curve is a geometric object that parametrizes isomorphism classes of elliptic curves together with some additional structure depending on some modular subgroup. The generalization that we will be interested in are the so called Shimura curves. We will be particularly interested in their p-adic models. In this thesis, we treat two different topics, one in each side of the Langlands program. In the Galois representations' side, we are interested in Galois representations that take values in local Hecke algebras attached to modular forms over finite fields. In the automorphic forms' side, we are interested in Shimura curves: we develop some arithmetic results in definite quaternion algebras and give some results about Mumford curves covering p-adic Shimura curves.
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Books on the topic "Finite fields (Algebra) Geometry, Projective"

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Projective geometries over finite fields. 2nd ed. Oxford: Clarendon Press, 1998.

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A, Thas J., ed. General Galois geometries. Oxford: Clarendon Press, 1991.

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Katcher, Pollatsek Harriet Suzanne, ed. Difference sets: Connecting algebra, combinatorics and geometry. Providence, Rhode Island: American Mathematical Society, 2013.

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Dmitri, Kaledin, and Tschinkel Yuri, eds. Higher-dimensional geometry over finite fields. Amsterdam, Netherlands: IOS Press, 2008.

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Noll, W. Finite-dimensional spaces: Algebra, geometry, and analysis. Dordrecht: M. Nijhoff, 1987.

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1971-, Orlik Sascha, and Rapoport M. 1948-, eds. Period domains over finite and p-adic fields. Cambridge: Cambridge University Press, 2010.

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Gary, McGuire, ed. Finite fields: Theory and applications : Ninth International Conference on Finite Fields and Applications, July 13-17, 2009, Dublin, Ireland. Providence, R.I: American Mathematical Society, 2010.

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Hansen, Søren Have. Rational points on curves over finite fields. [Aarhus, Denmark: Aarhus Universitet, Matematisk Institut, 1995.

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Many rational points: Coding theory and algebraic geometry. Dordrecht: Kluwer Academic Publishers, 2003.

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Artin, Emil. Algèbre géométrique. Paris: Editions Jacques Gabay, 1996.

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Book chapters on the topic "Finite fields (Algebra) Geometry, Projective"

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Gekeler, Ernst-Ulrich. "Asymptotically Optimal Towers of Curves over Finite Fields." In Algebra, Arithmetic and Geometry with Applications, 325–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18487-1_21.

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Farrán, J. I. "Asymptotics of Reduced Algebraic Curves Over Finite Fields." In Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 511–23. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96827-8_22.

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Eick, Bettina, and Tobias Moede. "Classifying Nilpotent Associative Algebras: Small Coclass and Finite Fields." In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 213–29. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70566-8_9.

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D'Agostino, Susan. "Conclusion." In How to Free Your Inner Mathematician, 293–98. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198843597.003.0048.

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This book offers a survey of mathematical topics. However, there is much more for you to explore. Catastrophe theory, the Chinese Remainder Theorem, combinatorics, and complex analysis. Equivalence relations, Euclid’s elements, and Euler’s formula. The Fields Medal and Four-color Theorem. Galois theory, the gambler’s fallacy, geodesic domes, the geometry of spacetime, and group theory. The Ham Sandwich Theorem. Isomorphisms. Linear algebra. The Mandelbrot set, mathematical induction, matrices, and the monster group. The parallel postulate, Pascal’s triangle, perfect numbers, permutation groups, pi, the Poincare Conjecture, projective geometry, public-key cryptography, and Pythagoras’ Theorem. Quaternions. Regression analysis. Set theory, squaring the circle, and surreal numbers. Truth tables, turning machines, and turning a sphere inside out. Venn diagrams. Wavelets. Zero. The list never ends....
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