000 | 02946nam a22004695i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/978-3-642-13368-8 _2doi |
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050 | 4 | _aQA251.3 | |
072 | 7 |
_aPBF _2bicssc |
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072 | 7 |
_aMAT002010 _2bisacsh |
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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. |
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300 |
_aX, 210 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1999 |
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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 |