AMS/IP Studies in Advanced Mathematics 1999; 529 pp; hardcover Volume: 11 ISBN10: 0821811908 ISBN13: 9780821811900 List Price: US$68 Member Price: US$54.40 Order Code: AMSIP/11
 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, Cambridge, MA. Readership Graduate students and research mathematicians working in arithmetic geometry. Table of Contents  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
 Bibliography
 Index
