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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.

## Publications

 Pub. Date ISBN-13 ISBN-10 Medium Binding Size, Etc. Status List Price 2018 Jan 9781470417413 1470417413 E-Book In Print 2015 Jan 9781470412265 1470412268 Print paperback In Print 1999 9780821811900 0821811908 Print hardcover In Print US\$68.00