Valuation theory of group rings and homology of soluble groups
Comparison between the different programs for local uniformization
Extensions of Noether's problem and Gelfand-Kirillov's conjecture to certain class...
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| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Missouri, Dept Math, Columbia, MO 65211 - USA
[2] Univ Fed Sao Carlos, Dept Matemat, Rodovia Washington Luis 235, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Mathematische Nachrichten; v. 294, n. 1, p. 15-37, JAN 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field(K,nu)and an extension omega of nu to a finite extensionLofK. Then we study when the valuation ring of omega is essentially finitely generated over the valuation ring of nu. We present a necessary condition in terms of classic invariants of the extension by Hagen Knaf and show that in some particular cases, this condition is also sufficient. We also study when the corresponding extension of graded algebras is finitely generated. For this problem we present an equivalent condition (which is weaker than the one for the finite generation of the valuation rings). (AU) | |
| FAPESP's process: | 17/17835-9 - The relation between toric geometry, theory of local blow-ups and ramification theory and their applications in valuation theory |
| Grantee: | Josnei Antonio Novacoski |
| Support Opportunities: | Research Grants - Young Investigators Grants |