The Use of Ultraproducts in Commutative Algebra
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 ultraprodu...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | Livre numérique |
| اللغة: | Anglais |
| منشور في: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| الطبعة: | 1st ed. 2010. |
| سلاسل: | Lecture Notes in Mathematics
1999 |
| الموضوعات: | |
| الوصول للمادة أونلاين: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| ملاحظة: |
L'impression du document génère 212 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The use of ultraproducts in commutative algebra, Hans Schoutens, Berlin, Springer, 2010, 1 vol. (X-204 p.), Lecture notes in mathematics, 978-3-642-13367-1 • The use of ultraproducts in commutative algebra, Hans Schoutens, Berlin, Springer, 2010, 1 vol. (X-204 p.), Lecture notes in mathematics, 978-3-642-13367-1 • The Use of Ultraproducts in Commutative Algebra, Texte imprimé, 9783642133695 |
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| 100 | 1 | |a Schoutens, Hans. | |
| 245 | 1 | 0 | |a The Use of Ultraproducts in Commutative Algebra |c Hans Schoutens. |
| 250 | |a 1st ed. 2010. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Lecture Notes in Mathematics |v 1999 |x 1617-9692 | |
| 500 | |a L'impression du document génère 212 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Ultraproduits | ||
| 650 | |a Algèbres commutatives | ||
| 650 | |a Mathématiques | ||
| 650 | |a Géométrie algébrique | ||
| 650 | |a Anneaux commutatifs | ||
| 776 | 0 | |0 147043832 |t The use of ultraproducts in commutative algebra |f Hans Schoutens |c Berlin |n Springer |d 2010 |p 1 vol. (X-204 p.) |s Lecture notes in mathematics |z 978-3-642-13367-1 | |
| 776 | 0 | |0 147043832 |t The use of ultraproducts in commutative algebra |f Hans Schoutens |c Berlin |n Springer |d 2010 |p 1 vol. (X-204 p.) |s Lecture notes in mathematics |z 978-3-642-13367-1 | |
| 776 | 0 | |t The Use of Ultraproducts in Commutative Algebra |b Texte imprimé |z 9783642133695 | |
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