Almost Ring Theory

  • Authors
  • Ofer Gabber
  • Lorenzo Ramero

Part of the Lecture Notes in Mathematics book series (LNM, volume 1800)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Ofer Gabber, Lorenzo Ramero
    Pages 1-10
  3. Ofer Gabber, Lorenzo Ramero
    Pages 11-49
  4. Ofer Gabber, Lorenzo Ramero
    Pages 50-91
  5. Ofer Gabber, Lorenzo Ramero
    Pages 92-129
  6. Ofer Gabber, Lorenzo Ramero
    Pages 130-194
  7. Ofer Gabber, Lorenzo Ramero
    Pages 195-241
  8. Ofer Gabber, Lorenzo Ramero
    Pages 242-286
  9. Ofer Gabber, Lorenzo Ramero
    Pages 287-300
  10. Ofer Gabber, Lorenzo Ramero
    Pages 301-303
  11. Back Matter
    Pages 304-307

About this book


This book develops thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions.

The reader is assumed to be familiar with general categorical notions, some basic commutative algebra and some advanced homological algebra (derived categories, simplicial methods). Apart from these general prerequisites, the text is as self-contained as possible. One novel feature of the book - compared with Faltings' earlier treatment - is the systematic exploitation of the cotangent complex, especially for the study of deformations of almost algebras.


Algebra Almost rings Homological algebra deformations rigid geometry ring theory valuations

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-40594-8
  • Online ISBN 978-3-540-45096-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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