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＜電子ブック＞
Almost Ring Theory / by Ofer Gabber, Lorenzo Ramero
(Lecture Notes in Mathematics. ISSN:16179692 ; 1800)

版	1st ed. 2003.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2003
大きさ	VI, 318 p : online resource
著者標目	*Gabber, Ofer author Ramero, Lorenzo author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic geometry LCSH:Algebra, Homological LCSH:Algebraic fields LCSH:Polynomials FREE:Algebra FREE:Commutative Rings and Algebras FREE:Algebraic Geometry FREE:Category Theory, Homological Algebra FREE:Field Theory and Polynomials
一般注記	Introduction -- Homological Theory -- Almost Ring Theory -- Fine Study of Almost Projective Modules -- Henselian Pairs -- Valuation Theory -- Analytic Geometry -- Appendix -- References -- Index 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 HTTP:URL=https://doi.org/10.1007/b10047

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