Almost Ring Theory [electronic resource] /
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.
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Format: | Texto biblioteca |
Language: | eng |
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Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
2003
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Subjects: | Mathematics., Algebra., Algebraic geometry., Category theory (Mathematics)., Homological algebra., Commutative algebra., Commutative rings., Field theory (Physics)., Commutative Rings and Algebras., Algebraic Geometry., Category Theory, Homological Algebra., Field Theory and Polynomials., |
Online Access: | http://dx.doi.org/10.1007/b10047 |
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KOHA-OAI-TEST:2177772018-07-30T23:54:05ZAlmost Ring Theory [electronic resource] / Gabber, Ofer. author. Ramero, Lorenzo. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,2003.engThis 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.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.Mathematics.Algebra.Algebraic geometry.Category theory (Mathematics).Homological algebra.Commutative algebra.Commutative rings.Field theory (Physics).Mathematics.Algebra.Commutative Rings and Algebras.Algebraic Geometry.Category Theory, Homological Algebra.Field Theory and Polynomials.Springer eBookshttp://dx.doi.org/10.1007/b10047URN:ISBN:9783540450962 |
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Mathematics. Algebra. Algebraic geometry. Category theory (Mathematics). Homological algebra. Commutative algebra. Commutative rings. Field theory (Physics). Mathematics. Algebra. Commutative Rings and Algebras. Algebraic Geometry. Category Theory, Homological Algebra. Field Theory and Polynomials. Mathematics. Algebra. Algebraic geometry. Category theory (Mathematics). Homological algebra. Commutative algebra. Commutative rings. Field theory (Physics). Mathematics. Algebra. Commutative Rings and Algebras. Algebraic Geometry. Category Theory, Homological Algebra. Field Theory and Polynomials. |
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Mathematics. Algebra. Algebraic geometry. Category theory (Mathematics). Homological algebra. Commutative algebra. Commutative rings. Field theory (Physics). Mathematics. Algebra. Commutative Rings and Algebras. Algebraic Geometry. Category Theory, Homological Algebra. Field Theory and Polynomials. Mathematics. Algebra. Algebraic geometry. Category theory (Mathematics). Homological algebra. Commutative algebra. Commutative rings. Field theory (Physics). Mathematics. Algebra. Commutative Rings and Algebras. Algebraic Geometry. Category Theory, Homological Algebra. Field Theory and Polynomials. Gabber, Ofer. author. Ramero, Lorenzo. author. SpringerLink (Online service) Almost Ring Theory [electronic resource] / |
description |
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. |
format |
Texto |
topic_facet |
Mathematics. Algebra. Algebraic geometry. Category theory (Mathematics). Homological algebra. Commutative algebra. Commutative rings. Field theory (Physics). Mathematics. Algebra. Commutative Rings and Algebras. Algebraic Geometry. Category Theory, Homological Algebra. Field Theory and Polynomials. |
author |
Gabber, Ofer. author. Ramero, Lorenzo. author. SpringerLink (Online service) |
author_facet |
Gabber, Ofer. author. Ramero, Lorenzo. author. SpringerLink (Online service) |
author_sort |
Gabber, Ofer. author. |
title |
Almost Ring Theory [electronic resource] / |
title_short |
Almost Ring Theory [electronic resource] / |
title_full |
Almost Ring Theory [electronic resource] / |
title_fullStr |
Almost Ring Theory [electronic resource] / |
title_full_unstemmed |
Almost Ring Theory [electronic resource] / |
title_sort |
almost ring theory [electronic resource] / |
publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, |
publishDate |
2003 |
url |
http://dx.doi.org/10.1007/b10047 |
work_keys_str_mv |
AT gabberoferauthor almostringtheoryelectronicresource AT ramerolorenzoauthor almostringtheoryelectronicresource AT springerlinkonlineservice almostringtheoryelectronicresource |
_version_ |
1756269799063683072 |