000 02946nam a22004695i 4500
001 978-3-642-13368-8
003 DE-He213
005 20190213151312.0
007 cr nn 008mamaa
008 100716s2010 gw | s |||| 0|eng d
020 _a9783642133688
_9978-3-642-13368-8
024 7 _a10.1007/978-3-642-13368-8
_2doi
050 4 _aQA251.3
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512.44
_223
100 1 _aSchoutens, Hans.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Use of Ultraproducts in Commutative Algebra
_h[electronic resource] /
_cby Hans Schoutens.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aX, 210 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 ;
_v1999
505 0 _aUltraproducts and ?o?’ Theorem -- Flatness -- Uniform Bounds -- Tight Closure in Positive Characteristic -- Tight Closure in Characteristic Zero. Affine Case -- Tight Closure in Characteristic Zero. Local Case -- Cataproducts -- Protoproducts -- Asymptotic Homological Conjectures in Mixed Characteristic.
520 _aIn spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.
650 0 _aAlgebra.
650 0 _aGeometry, algebraic.
650 1 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
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642133671
776 0 8 _iPrinted edition:
_z9783642133695
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1999
856 4 0 _uhttps://doi.org/10.1007/978-3-642-13368-8
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10207
_d10207