Analytic methods in arithmetic geometry : Arizona Winter School 2016, Analytic Methods in Arithmetic Geometry, March 12-16, 2016, the University of Arizona, Tucson, AZ
著者
書誌事項
Analytic methods in arithmetic geometry : Arizona Winter School 2016, Analytic Methods in Arithmetic Geometry, March 12-16, 2016, the University of Arizona, Tucson, AZ
（Contemporary mathematics, 740 . Centre de Recherches Mathématiques proceedings）
American Mathematical Society, c2019
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注記
Includes bibliographical references
内容説明・目次
内容説明
This volume contains the proceedings of the Arizona Winter School 2016, which was held from March 12-16, 2016, at The University of Arizona, Tucson, AZ. In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with $\mathrm{SL}_2(\mathbb{F}_q)$ and some of its subgroups as the key examples. The article by Etienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from $\ell$-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic $L$-functions, and Mumford-Tate groups.
目次
A. C. Cojocaru, Primes, elliptic curves and cyclic groups
H. A. Helfgott, Growth and expansion in algebraic groups over finite fields
E. Fouvry, E. Kowalski, P. Michel, and W. Sawin, Lectures on applied $\ell$-adic cohomology
A. V. Sutherland, Sato-Tate distributions.
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