| Almost Ring Theory 2003 Edition Contributor(s): Gabber, Ofer (Author), Ramero, Lorenzo (Author) |
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ISBN: 3540405941 ISBN-13: 9783540405948 Publisher: Springer OUR PRICE: $75.99 Product Type: Paperback - Other Formats Published: August 2003 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - General - Mathematics | Geometry - Algebraic - Mathematics | Algebra - Abstract |
| Dewey: 512.44 |
| LCCN: 2003057372 |
| Series: Lecture Notes in Mathematics |
| Physical Information: 0.68" H x 6.14" W x 9.21" (1.00 lbs) 318 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The authors develop 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. |