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Record Nr. |
UNINA9910144601603321 |
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Autore |
Gabber Ofer |
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Titolo |
Almost Ring Theory / / by Ofer Gabber, Lorenzo Ramero |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2003 |
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ISBN |
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Edizione |
[1st ed. 2003.] |
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Descrizione fisica |
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1 online resource (VI, 318 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1800 |
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Disciplina |
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Soggetti |
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Algebra |
Commutative algebra |
Commutative rings |
Algebraic geometry |
Category theory (Mathematics) |
Homological algebra |
Field theory (Physics) |
Commutative Rings and Algebras |
Algebraic Geometry |
Category Theory, Homological Algebra |
Field Theory and Polynomials |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Introduction -- Homological Theory -- Almost Ring Theory -- Fine Study of Almost Projective Modules -- Henselian Pairs -- Valuation Theory -- Analytic Geometry -- Appendix -- References -- Index. |
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Sommario/riassunto |
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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 |
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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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