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Softcover ISBN:  9781470412265 
Product Code:  AMSIP/11.S 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $64.80 
eBook ISBN:  9781470417413 
Product Code:  AMSIP/11.E 
List Price:  $76.00 
MAA Member Price:  $68.40 
AMS Member Price:  $60.80 
Softcover ISBN:  9781470412265 
eBook ISBN:  9781470417413 
Product Code:  AMSIP/11.S.B 
List Price:  $157.00 $119.00 
MAA Member Price:  $141.30 $107.10 
AMS Member Price:  $125.60 $95.20 

Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 11; 1999; 529 ppMSC: Primary 14
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 SerreTate 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 SerreTate 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.
Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA.
ReadershipGraduate students and research mathematicians working in arithmetic geometry.

Table of Contents

Chapters

Introduction

Crysstable bundles

Torally Crysstable bundles in positive characteristic

VFpatterns

Construction of examples

Combinatorialization at infinity of the stack of nilcurves

The stack of quasianalytic selfisogenies

The generalized ordinary theory

The geometrization of binaryordinary Frobenius liftings

The geometrization of spiked Frobenius liftings

Representations of the fundamental group of the curve

Ordinary stable bundles on a curve


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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 SerreTate 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 SerreTate 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.
Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA.
Graduate students and research mathematicians working in arithmetic geometry.

Chapters

Introduction

Crysstable bundles

Torally Crysstable bundles in positive characteristic

VFpatterns

Construction of examples

Combinatorialization at infinity of the stack of nilcurves

The stack of quasianalytic selfisogenies

The generalized ordinary theory

The geometrization of binaryordinary Frobenius liftings

The geometrization of spiked Frobenius liftings

Representations of the fundamental group of the curve

Ordinary stable bundles on a curve