Imaginaries in Separably Closed Valued Fields

Basic data for this talk

Type of talk: scientific Talk

Name der Vortragenden: Hils, Martin

Date of talk: 29/03/2019

Talk language: English

URL of slides: https://www.youtube.com/watch?v=C3UY-vpGzF4&feature=youtu.be

Information about the event

Name of the event: Kolchin Seminar in Differential Algebra

Event period: 29/03/2019

Event location: The Graduate Center - CUNY, New York, USA

Event website: http://qcpages.qc.cuny.edu/~aovchinnikov/ksda/spring2019.php

Abstract

Let p be a fixed prime number and let SCVFp be the first order theory of separably closed non-trivially valued fields of characteristic p. In the talk, we will see that, in many ways, from a model-theoretic point of view, the step from algebraically closed VALUED fields in characteristic p to SCVFp is not more complicated than the one from algebraically closed fields to separably closed fields in characteristic p. At a basic level, this is true for quantifier elimination (Delon), for which it suffices to add parametrized p-coordinate functions to any of the usual languages for valued fields. At a more sophisticated level, in finite degree of imperfection, when a p-basis is named by constants or when one just works with Hasse derivations, the imaginaries (i.e. definable quotients) are classified by so-called the geometric sorts of Haskell-Hrushovski-Macpherson, certain higher-dimensional analogs of the residue field and the value group. This classification is proved by a reduction to the algebraically closed case, using prolongations. This is joint work with Moshe Kamensky and Silvain Rideau.

Keywords: Model Theory; Separably Closed Valued Fields; Imaginaries