Homotopy theory is founded on the idea of contracting the interval, either as a space, or as an actual homotopy, i.e., a path in a space of maps. In algebraic geometry, the affine line A1k serves as an algebraic equivalent of the interval, at least in characteristic 0. Matters di ffer in characteristic p > 0 where 1(A1k) is an in finite group. This raises the question whether there is an etale contractible variety in positive characteristic. In this talk, we show that there are no non-trivial smooth varieties over an algebraically closed field k of characteristic p > 0 that are contractible in the sense of etale homotopy theory. This talk is based on joint work with Johannes Schmidt and Jakob Stix.
Mittwoch, den 26. März 2014 um 10.30-11.30 Uhr, in INF288, HS2 Mittwoch, den 26. März 2014 at 10.30-11.30, in INF288, HS2
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Alexander Schmidt, Jakob Stix