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Table of contents (9 chapters)
Keywords
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.
Bibliographic Information
Book Title: Almost Ring Theory
Authors: Ofer Gabber, Lorenzo Ramero
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b10047
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2003
Softcover ISBN: 978-3-540-40594-8Published: 11 August 2003
eBook ISBN: 978-3-540-45096-2Published: 09 December 2003
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VI, 318
Topics: Algebra, Commutative Rings and Algebras, Algebraic Geometry, Category Theory, Homological Algebra, Field Theory and Polynomials