unipd

COLLOQUIA PATAVINA

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Model theory of fields and some of its applications
Elisabeth Bouscaren
8.06.2010



Abstract

Model Theory is a branch of Mathematical Logic which is relatively recent and  still not very well-known, in spite of its strong links to algebra and geometry. We will first try to present the very basic notions (definable sets, compactness, transfer principles) through some classical examples of applications of the model theory of fields (in particular, the transfer theorems  of Ax-Kochen-Ersov  about Henselian valued  fields and their application to a conjecture of Artin in the 60's). We will then present some recents applications of model theory, focusing on the interactions with number theory and algebraic geometry.