## COLLOQUIA PATAVINA |

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.