Josnei NOVACOSKI – Extension of valuation rings and associated graded algebras

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Date/heure
Date(s) - 16/01/2020
14 h 00 min - 15 h 00 min

Emplacement
FRUMAM, St Charles

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Josnei NOVACOSKI (Universidade Federal de São Carlos, UFSCar, Brazil)

The main goal of this talk  is to present 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 extension $L$ of $K$. 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 and show that in some particular cases, this condition is also sufficient. We also discuss 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).

This is a joint work with Steven Dale Cutkosky.


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