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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 differ in characteristic p > 0 where 1(A1k) is an infinite 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