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Seminario di algebra: “Non-compact subsets of the Zariski space”

Martedì 4 Dicembre 2018, ore 15:00 - Sala Riunioni 701 - Dario Spirito

ARGOMENTI: Seminars

Martedì 4 Dicembre 2018 alle ore 15:00 in Sala Riunioni 701, Dario Spirito (Università degli Studi Roma Tre) terràun seminario dal titolo “Non-compact subsets of the Zariski space”.

Abstract
The Zariski space Zar(K|D) of a field K over an integral domain D (with D ⊆ K) is the set of all valuation rings containing D having K as quotient field. Zariski studied this space from a topological point of view during its study of the problem of resolution of singularities; in this context, his most important result was the fact that Zar(K|D) is always a compact space. In this talk, I will present some methods to determine subspaces of Zar(K|D) that are not compact; in particular, I will show how to characterize which extensions D ⊆ K give rise to a Noetherian Zariski space (where a topological space is Noetherian if all its subsets are compact).