P-Adic Automorphic Forms on Shimura Varieties 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2025

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Hida, Haruzo 作者

Springer Verlag

译者

2004-5 出版日期

401 页数

$ 190.97 价格

HRD

丛书系列

9780387207117 图书编码

P-Adic Automorphic Forms on Shimura Varieties 在线电子书图书标签: 数学

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发表于2025-01-10

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P-Adic Automorphic Forms on Shimura Varieties 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2025

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P-Adic Automorphic Forms on Shimura Varieties 在线电子书图书描述

This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1. An elementary construction of Shimura varieties as moduli of abelian schemes 2. p-adic deformation theory of automorphic forms on Shimura varieties 3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety The book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others). Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000).

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