Ehud Hrushovski - 2015

Ehud Hrushovsi (University of de Jerusalem) offers a second course intitled Towards a model theory of global fields every Wednesday morning from 10 to 12 , from January 2016 to April 2016, at the Institut Henri Poincaré (11 rue Pierre et Marie Curie - 75005 Paris)

Agenda

- 13/01 : amphitheatre Hermite
- 20/01 : room 314
- 27/01 : amphitheatre Hermite
- 03/02 : room 314
- 10/02 : room 314
- 17/02 : room 314
- 09/03 : room 314 (cancelled and postponed on April, 13th)
- 16/03 : room 314
- 30/03 : room 314
- 06/04 : room 314
- 13/04 : room 201

Abstract

Beyond the sum of the local geometries associated with each place of a field, there is a fascinating global geometry arising from their interaction. As recognized by Artin-Whaples in the discrete setting, this interaction is governed by a simple relation among the places, the product formula. I will describe a model-theoretic framework, developed jointly with Itai Ben Yaacov, able to axiomatize this relation. We will see that an even preliminary model-theoretic investigation leads to deep algebro-geometric structures associated with cones of divisors and curves. This class will concentrate on the purely non-archimedean case; the field $\Cc(t)^{alg}$, with a height function into $\Rr$, is an example. We will show that it is existentially closed. The first half of the class will be an introduction to the required elements of convexity theory and algebraic geometry.