The Use of Ultraproducts in Commutative Al...

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Sprache: Englisch

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Beschreibung

In 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.

Inhaltsverzeichnis

Ultraproducts 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.

Details

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	x 210 S.
ISBN-13:	9783642133671
ISBN-10:	3642133673
Sprache:	Englisch
Herstellernummer:	978-3-642-13367-1
Einband:	Kartoniert / Broschiert
Autor:	Schoutens, Hans
Hersteller:	Springer Springer, Berlin
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Abbildungen:	X, 210 p.
Maße:	236 x 151 x 14 mm
Von/Mit:	Hans Schoutens
Erscheinungsdatum:	31.07.2010
Gewicht:	0,342 kg