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AMS/IP Studies in Advanced Mathematics

Volume 11

Foundations of p-adic Teichmüller Theory

Original Publication: 1999

Publisher: American Mathematical Society / International Press

Language: English

Paperback

529 pages

Description

This book lays the foundation for a theory of uniformization of p–adic hyperbolic curves and their moduli. On one hand, this theory generalizes the Fuchsian and Bers uniformizations of complex hyperbolic curves and their moduli to nonarchimedian places. That is why in this book, the theory is referred to as p–adic Teichmüller theory, for short. On the other hand, the theory may be regarded as a fairly precise hyperbolic analog of the Serre-Tate theory of ordinary abelian varieties and their moduli.

The theory of uniformization of p–adic hyperbolic curves and their moduli was initiated in a previous work by Mochizuki. And in some sense, this book is a continuation and generalization of that work. This book aims to bridge the gap between the approach presented and the classical uniformization of a hyperbolic Riemann surface that is studied in undergraduate complex analysis.

Features:

• Presents a systematic treatment of the moduli space of curves from the point of view of $p$-adic Galois representations.

• Treats the analog of Serre-Tate theory for hyperbolic curves.

• Develops a p–adic analog of Fuchsian and Bers uniformization theories.

• Gives a systematic treatment of a “nonabelian example” of p–adic Hodge theory.

This volume is part of the AMS/IP Studies in Advanced Mathematics book series.

Publications

Pub. Date

ISBN-13

ISBN-10

Medium

Binding

Size, Etc.

Status

List Price

2015 Jan

9781470412265

1470412268

Print

paperback

In Print

1999

9780821811900

0821811908

Print

hardcover

In Print

US$68.00