The Use of Ultraproducts in Commutative Algebra [recurso electrónico] / by Hans Schoutens.

Por: Schoutens, Hans [author.]Colaborador(es): SpringerLink (Online service)Tipo de material: TextoTextoSeries Lecture Notes in Mathematics ; 1999Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010Descripción: X, 204p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642133688Tema(s): Mathematics | Geometry, algebraic | Algebra | Mathematics | Commutative Rings and Algebras | Algebraic GeometryFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 512.44 Clasificación LoC:QA251.3Recursos en línea: Libro electrónicoTexto
Contenidos:
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.
En: Springer eBooksResumen: 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.
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Libro Electrónico Biblioteca Electrónica
Colección de Libros Electrónicos QA251.3 (Browse shelf(Abre debajo)) 1 No para préstamo 374472-2001

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.

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.

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