Analytic Methods in Arithmetic Geometry

Alina Bucur

ISBN 10: 1470437848 / ISBN 13: 9781470437848

Published by American Mathematical Society, US, 2020

About this Item

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.

Seller Inventory # LU-9781470437848

Bibliographic Details

• Title: Analytic Methods in Arithmetic Geometry
• Publisher: American Mathematical Society, US
• Publication Date: 2020
• Language: English
• ISBN 10: 1470437848
• ISBN 13: 9781470437848
• Binding: Paperback
• Condition: New
• Weight: 460 grams

About this title

Synopsis

The volume collects notes from the lectures presented during the March 2016 Arizona Winter School on analytic methods in arithmetic geometry. The four lectures survey results about rational primes viewed in the context of elliptic curves, introduce growth and expansion in algebraic groups of Lie type over finite fields, describe how the systematic use of deep methods from l-adic cohomology has advanced analytic number theory, and explore the relationship between Galois representations, Mumford-Tate groups, and Sato-Tate distributions. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)