The Use of Ultraproducts in Commutative Algebra: Lecture Notes in Mathematics, cartea 1999
Autor Hans Schoutensen Limba Engleză Paperback – 31 iul 2010
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Specificații
ISBN-13: 9783642133671
ISBN-10: 3642133673
Pagini: 210
Ilustrații: X, 210 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.32 kg
Ediția:2010
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3642133673
Pagini: 210
Ilustrații: X, 210 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.32 kg
Ediția:2010
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics
Locul publicării:Berlin, Heidelberg, Germany
Public țintă
ResearchCuprins
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.
Textul de pe ultima copertă
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.
Caracteristici
Novel use of ultraproducts in algebra Provides a gentle introduction to tight closure in characteristic zero Contains a survey chapter on various flatness criteria Includes supplementary material: sn.pub/extras