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Record Nr. |
UNISA996466512503316 |
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Autore |
Schoutens Hans |
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Titolo |
The Use of Ultraproducts in Commutative Algebra [[electronic resource] /] / by Hans Schoutens |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2010 |
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ISBN |
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1-280-39178-2 |
9786613569707 |
3-642-13368-1 |
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Edizione |
[1st ed. 2010.] |
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Descrizione fisica |
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1 online resource (X, 210 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1999 |
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Classificazione |
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60G5160E0760J8045K0565N3028A7860H0560G5760J7526A33 |
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Disciplina |
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Soggetti |
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Commutative algebra |
Commutative rings |
Algebraic geometry |
Commutative Rings and Algebras |
Algebraic Geometry |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (p. 193-197) and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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