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Foundations of $p$-adic Teichmüller Theory
 
Shinichi Mochizuki Research Institute for the Mathematical Sciences, Kyoto, Japan
A co-publication of the AMS and International Press of Boston
Foundations of p-adic Teichmuller Theory
Softcover ISBN:  978-1-4704-1226-5
Product Code:  AMSIP/11.S
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $64.80
eBook ISBN:  978-1-4704-1741-3
Product Code:  AMSIP/11.E
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $60.80
Softcover ISBN:  978-1-4704-1226-5
eBook: ISBN:  978-1-4704-1741-3
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
Foundations of p-adic Teichmuller Theory
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Foundations of $p$-adic Teichmüller Theory
Shinichi Mochizuki Research Institute for the Mathematical Sciences, Kyoto, Japan
A co-publication of the AMS and International Press of Boston
Softcover ISBN:  978-1-4704-1226-5
Product Code:  AMSIP/11.S
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $64.80
eBook ISBN:  978-1-4704-1741-3
Product Code:  AMSIP/11.E
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $60.80
Softcover ISBN:  978-1-4704-1226-5
eBook ISBN:  978-1-4704-1741-3
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 Details
     
     
    AMS/IP Studies in Advanced Mathematics
    Volume: 111999; 529 pp
    MSC: 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 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.

    Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

    Readership

    Graduate students and research mathematicians working in arithmetic geometry.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Crys-stable bundles
    • Torally Crys-stable bundles in positive characteristic
    • VF-patterns
    • Construction of examples
    • Combinatorialization at infinity of the stack of nilcurves
    • The stack of quasi-analytic self-isogenies
    • The generalized ordinary theory
    • The geometrization of binary-ordinary Frobenius liftings
    • The geometrization of spiked Frobenius liftings
    • Representations of the fundamental group of the curve
    • Ordinary stable bundles on a curve
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 111999; 529 pp
MSC: 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 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.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

Readership

Graduate students and research mathematicians working in arithmetic geometry.

  • Chapters
  • Introduction
  • Crys-stable bundles
  • Torally Crys-stable bundles in positive characteristic
  • VF-patterns
  • Construction of examples
  • Combinatorialization at infinity of the stack of nilcurves
  • The stack of quasi-analytic self-isogenies
  • The generalized ordinary theory
  • The geometrization of binary-ordinary Frobenius liftings
  • The geometrization of spiked Frobenius liftings
  • Representations of the fundamental group of the curve
  • Ordinary stable bundles on a curve
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.