Almost Ring Theory

by Ofer Gabber, Lorenzo Ramero

Overview

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.

Product Details

ISBN-13:	9783540405948
Publisher:	Springer Berlin Heidelberg
Publication date:	09/29/2003
Series:	Lecture Notes in Mathematics , #1800
Edition description:	2003
Pages:	318
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Introduction.- Homological Theory.- Almost Ring Theory.- Fine Study of Almost Projective Modules.- Henselian Pairs.- Valuation Theory.- Analytic Geometry.- Appendix.- References.- Index.