Lectures on Formal and Rigid Geometry

  • Siegfried Bosch

Part of the Lecture Notes in Mathematics book series (LNM, volume 2105)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Siegfried Bosch
    Pages 1-5
  3. Classical Rigid Geometry

    1. Front Matter
      Pages 7-7
    2. Siegfried Bosch
      Pages 9-29
    3. Siegfried Bosch
      Pages 31-63
    4. Siegfried Bosch
      Pages 65-91
    5. Siegfried Bosch
      Pages 93-116
    6. Siegfried Bosch
      Pages 117-147
  4. Formal Geometry

    1. Front Matter
      Pages 149-149
    2. Siegfried Bosch
      Pages 151-173
    3. Siegfried Bosch
      Pages 175-214
    4. Siegfried Bosch
      Pages 215-227
  5. Back Matter
    Pages 229-256

About this book


A first version of this work appeared in 2005 as a Preprint of the Collaborative Research Center "Geometrical Structures in Mathematics" at the University of Münster. Its aim was to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work.

This Lecture Notes Volume is a revised and slightly expanded version of the original preprint and has been published at the suggestion of several experts in the field.


Formal blowing-up Formal scheme Rigid analytic space Tate algebra Tate's Acyclicity Theorem

Authors and affiliations

  • Siegfried Bosch
    • 1
  1. 1.Westfälische Wilhelms-Universität Mathematisches InstitutMünsterGermany

Bibliographic information