(?xp)-adic Discrete Subgroup
(AcA^Azxp)-adic Discrete Subgroup
A01=Yasutaka Ihara
Arithmetic Fundamental Group
Author_Yasutaka Ihara
Category=PBCN
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Non-Abelian Class Field Theory
Schwarzian Equation Defining Uniformization of Arithmetic Family of Curves and Reduction Mod p
Selberg-Type Zeta Function
Shimura Curves
Supersingularity and Rationality
Towers of Curves Over Finite Fields
Product details
- ISBN 9784931469501
- Publication Date: 03 Jan 2009
- Publisher: Mathematical Society of Japan
- Publication City/Country: JP
- Product Form: Paperback
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It is now well-known that the group SL2(Z[1/p]) and the system of modular curves over Fp2 are “closely related”, and that the latter provided first “examples” of curves over finite fields having many rational points. However, the “three basic relationships”, which really justify the former to be called the arithmetic fundamental group of the latter, still do not seem to be so commonly known.This book consists of two parts; a reproduction of the author's unpublished Lecture Notes (1968,69), and Author's Notes (2008). The former starts with explicit three main conjectural relationships for more general cases and gives various approaches towards their proofs. Though remained formally unpublished, these Lecture Notes had been widely circulated and have stimulated researches in various directions. The main conjectures themselves have also been proved since then. The Author's Notes (2008) gives detailed explanations of these developments, together with open problems.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
