MS Seminar (Mathematics - String Theory)

Speaker: Oliver Lorscheid (IMPA)
Title: A problem of Jacques Tits and Chevalley groups over F1
Date: Tue, Nov 06, 2012, 13:15 - 14:45
Place: Seminar Room A
Abstract: One of the main motivations of F1-geometry is to explain the analogy between Chevalley groups over finite fields and the combinatorial geometry of their Weyl groups. The idea to explain the combinatorial part as a geometry over an elusive field, which is nowadays called F1, "the field with one element", goes back to a paper of Jacques Tits from 1956.

This idea entered the flourishing area of F1-geometry as the formula G(F1)=W, and many authors contributed to it. However, the viewpoint that the F1-rational points of a Chevalley group G should equal its Weyl group W faces a certain functorial problem.

After giving a general introduction into the problem and the ideas of F1-geometry, I will explain how the framework of blueprints provides a natural solution to the problem. In particular, I will introduce the so-called Tits-category, which contains models of Chevalley groups over F1 that yield the Weyl groups in a functorial way.