Alina Bucur, David Zureick-Brown Analytic Methods in Arithmetic Geometry 9781470437848

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Автор: Alina Bucur, David Zureick-Brown
Название: Analytic Methods in Arithmetic Geometry
ISBN: 9781470437848
Издательство: Mare Nostrum (Eurospan)
Классификация:

Алгебра

Теория чисел

Геометрия

Алгебраическая геометрия

ISBN-10: 1470437848
Обложка/Формат: Paperback
Страницы: 248
Вес: 0.15 кг.
Дата издания: 28.02.2020
Серия: Contemporary mathematics
Язык: English
Размер: H 254 X W 178
Ключевые слова: Algebra,Algebraic geometry,Number theory
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Поставляется из: Англии
Описание: 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. Cojocarus 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. Helfgotts 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.
Дополнительное описание: Algebra|Algebraic geometry|Number theory

Analytic Methods in Arithmetic Geometry, Alina Bucur, David Zureick-Brown