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Essentially finite generation of valuation rings in terms of classical invariants

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  • Steven Dale Cutkosky
  • Josnei Novacoski

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,ν) and an extension ω of ν to a finite extension L of K. Then we study when the valuation ring of ω is essentially finitely generated over the valuation ring of ν. 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).

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  • Steven Dale Cutkosky & Josnei Novacoski, 2021. "Essentially finite generation of valuation rings in terms of classical invariants," Mathematische Nachrichten, Wiley Blackwell, vol. 294(1), pages 15-37, January.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:1:p:15-37
    DOI: 10.1002/mana.201900287
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    Cited by:

    1. Rankeya Datta, 2023. "Essential finite generation of extensions of valuation rings," Mathematische Nachrichten, Wiley Blackwell, vol. 296(3), pages 1041-1055, March.

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