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  • Book
  • © 2003

Almost Ring Theory

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-vi
  2. 1. Introduction

    • Ofer Gabber, Lorenzo Ramero
    Pages 1-10
  3. 2. Homological theory

    • Ofer Gabber, Lorenzo Ramero
    Pages 11-49
  4. 3. Almost ring theory

    • Ofer Gabber, Lorenzo Ramero
    Pages 50-91
  5. 4. Fine study of almost projective modules

    • Ofer Gabber, Lorenzo Ramero
    Pages 92-129
  6. 5. Henselization and completion of almost algebras

    • Ofer Gabber, Lorenzo Ramero
    Pages 130-194
  7. 6. Valuation theory

    • Ofer Gabber, Lorenzo Ramero
    Pages 195-241
  8. 7. Analytic geometry

    • Ofer Gabber, Lorenzo Ramero
    Pages 242-286
  9. 8. Appendix

    • Ofer Gabber, Lorenzo Ramero
    Pages 287-300
  10. References and Index

    • 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.

Keywords

  • Algebra
  • Almost rings
  • Homological algebra
  • deformations
  • rigid geometry
  • ring theory
  • valuations

Bibliographic Information

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions