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Title: Essentially finite generation of valuation rings in terms of classical invariants
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 and an extension ω of ν to a finite extensionLofK. 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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Award ID(s):
1700046
PAR ID:
10240814
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Mathematische Nachrichten
Volume:
294
Issue:
1
ISSN:
0025-584X
Page Range / eLocation ID:
p. 15-37
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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