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024 7 $a10.1007/b10047
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035   $a(DE-He213)978-3-540-45096-2
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100   $a20150519d2003      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aAlmost Ring Theory$b[electronic resource] /$fby Ofer Gabber, Lorenzo Ramero
205   $a1st ed. 2003.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003.
215   $a1 online resource (VI, 318 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1800
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-40594-1 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- Homological Theory -- Almost Ring Theory -- Fine Study of Almost Projective Modules -- Henselian Pairs -- Valuation Theory -- Analytic Geometry -- Appendix -- References -- Index.
330   $aThis book develops thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions. The reader is assumed to be familiar with general categorical notions, some basic commutative algebra and some advanced homological algebra (derived categories, simplicial methods). Apart from these general prerequisites, the text is as self-contained as possible. One novel feature of the book - compared with Faltings' earlier treatment - is the systematic exploitation of the cotangent complex, especially for the study of deformations of almost algebras.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1800
606   $aAlgebra
606   $aCommutative algebra
606   $aCommutative rings
606   $aAlgebraic geometry
606   $aCategory theory (Mathematics)
606   $aHomological algebra
606   $aField theory (Physics)
606   $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
606   $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051
615  0$aAlgebra.
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAlgebraic geometry.
615  0$aCategory theory (Mathematics).
615  0$aHomological algebra.
615  0$aField theory (Physics).
615 14$aAlgebra.
615 24$aCommutative Rings and Algebras.
615 24$aAlgebraic Geometry.
615 24$aCategory Theory, Homological Algebra.
615 24$aField Theory and Polynomials.
676   $a510
700   $aGabber$b Ofer$4aut$4http://id.loc.gov/vocabulary/relators/aut$0149498
702   $aRamero$b Lorenzo$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466385403316
996   $aAlmost Ring Theory$92543722
997   $aUNISA