ENGLISH

Almost Ring Theory

By Ofer Gabber , Lorenzo Ramero (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2003
ISBN
3540405941, 9783540405948
DOI
10.1007/b10047
Open Library ID
OL9366435M
Language
english
Format
PDF
Filesize
5 MB (4761521 bytes)
Series
Lecture Notes in Mathematics 1800
Edition
1
Pages
318\314
Time added
2011-06-04 13:46:07
Commutative Rings and Algebras; Algebraic GeometryHomological Algebra; Field Theory and Polynomials

Description

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.

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