Almost Ring Theory : Lecture Notes in Mathematics - Ofer Gabber

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Almost Ring Theory

By: Ofer Gabber, Lorenzo Ramero

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Paperback | 1 September 2003

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324 Pages

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22.23 x 16.51 x 1.91

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The authors develop 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.

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You Can Find This Book In

Non-Fiction Mathematics Groups & Group Theory Algebra Geometry Algebraic Geometry

Introduction	p. 1
Homological theory	p. 11
Almost ring theory	p. 50
Fine study of almost projective modules	p. 92
Henselization and completion of almost algebras	p. 130
Valuation theory	p. 195
Analytic geometry	p. 242
Appendix	p. 287
References	p. 301
Index	p. 304
Table of Contents provided by Blackwell. All Rights Reserved.

Almost Ring Theory

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