000 03336nam a22005415i 4500
001 978-3-540-45096-2
003 DE-He213
005 20190213151902.0
007 cr nn 008mamaa
008 150519s2003 gw | s |||| 0|eng d
020 _a9783540450962
_9978-3-540-45096-2
024 7 _a10.1007/b10047
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aGabber, Ofer.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aAlmost Ring Theory
_h[electronic resource] /
_cby Ofer Gabber, Lorenzo Ramero.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2003.
300 _aVI, 318 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1800
505 0 _aIntroduction -- Homological Theory -- Almost Ring Theory -- Fine Study of Almost Projective Modules -- Henselian Pairs -- Valuation Theory -- Analytic Geometry -- Appendix -- References -- Index.
520 _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.
650 0 _aAlgebra.
650 0 _aGeometry, algebraic.
650 0 _aField theory (Physics).
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aCommutative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11043
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aCategory Theory, Homological Algebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11035
650 2 4 _aField Theory and Polynomials.
_0http://scigraph.springernature.com/things/product-market-codes/M11051
700 1 _aRamero, Lorenzo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540405948
776 0 8 _iPrinted edition:
_z9783662203729
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1800
856 4 0 _uhttps://doi.org/10.1007/b10047
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c12222
_d12222