Essentially finite generation of valuation rings in terms of classical invariants

Autor(es)

Cutkosky, Steven Dale ^[1] ; Novacoski, Josnei ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Mathematische Nachrichten; v. 294, n. 1, p. 15-37, JAN 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 17/17835-9 - As relações entre geometria tórica, teoria de blow-ups locais e teoria de ramificação e suas applicações em teoria das valorizações
• Beneficiário: Josnei Antonio Novacoski
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores