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Field name	Details
Dewey Class	512
Title	Almost Ring Theory ([EBook] /) / by Ofer Gabber, Lorenzo Ramero.
Author	Gabber, Ofer
Added Personal Name	Ramero, Lorenzo author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2003.
Physical Details	VI, 318 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1800
ISBN	9783540450962
Summary Note	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.:
Contents note	Introduction -- Homological Theory -- Almost Ring Theory -- Fine Study of Almost Projective Modules -- Henselian Pairs -- Valuation Theory -- Analytic Geometry -- Appendix -- References -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/b10047
Links to Related Works	Subject References: Algebra . Algebraic Geometry . Category Theory, Homological Algebra . Category theory (Mathematics) . Commutative algebra . Commutative rings . Commutative Rings and Algebras . Field Theory and Polynomials . Field theory (Physics) . Homological algebra . Mathematics . Authors: Gabber, Ofer . Ramero, Lorenzo . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512 .

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Almost Ring Theory

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