04133nam 22008295 450 991014460160332120230617035156.03-540-45096-310.1007/b10047(CKB)1000000000233129(SSID)ssj0000321237(PQKBManifestationID)11255494(PQKBTitleCode)TC0000321237(PQKBWorkID)10262862(PQKB)10326484(DE-He213)978-3-540-45096-2(MiAaPQ)EBC6283688(MiAaPQ)EBC5585127(Au-PeEL)EBL5585127(OCoLC)54021059(EXLCZ)99100000000023312920150519d2003 u| 0engurnn|008mamaatxtccrAlmost Ring Theory /by Ofer Gabber, Lorenzo Ramero1st ed. 2003.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2003.1 online resource (VI, 318 p.) Lecture Notes in Mathematics,0075-8434 ;1800Bibliographic Level Mode of Issuance: Monograph3-540-40594-1 Includes bibliographical references and index.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.Lecture Notes in Mathematics,0075-8434 ;1800AlgebraCommutative algebraCommutative ringsAlgebraic geometryCategory theory (Mathematics)Homological algebraField theory (Physics)Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Commutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Field Theory and Polynomialshttps://scigraph.springernature.com/ontologies/product-market-codes/M11051Algebra.Commutative algebra.Commutative rings.Algebraic geometry.Category theory (Mathematics).Homological algebra.Field theory (Physics).Algebra.Commutative Rings and Algebras.Algebraic Geometry.Category Theory, Homological Algebra.Field Theory and Polynomials.510Gabber Oferauthttp://id.loc.gov/vocabulary/relators/aut149498Ramero Lorenzoauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910144601603321Almost Ring Theory2543722UNINA