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Homotopy theory and arithmetic geometry

Connections for Women: Algebraic Topology January 23, 2014 - January 24, 2014

January 24, 2014 (01:15PM PST - 02:15PM PST)
Speaker(s): Kirsten Wickelgren (Georgia Institute of Technology)
Location: MSRI: Simons Auditorium
Video

Abstract

The solutions in \mathbb{C} to a system of polynomial equations form a nice topological space which is useful even for studying solutions to the polynomials over smaller fields such as R or even Q. To study solutions over Q or characteristic p fields, it is more useful to replace the notion of topological space with an object in a suitable category where one can do homotopy theory, such as the Morel-Voevodsky category for A^1 homotopy theory, and pro-spaces, where one has the étale homotopy type of a scheme. We will define A^1 homotopy theory, étale topological type, and an étale realization between them of Isaksen. We will use this to discuss Grothendieck's anabelian conjectures and obstructions to solutions to polynomial equations

Supplements
19853?type=thumb Wickelgren 117 KB application/pdf Download
Video/Audio Files

v1222

H.264 Video v1222.mp4 350 MB video/mp4 rtsp://videos.msri.org/data/000/019/673/original/v1222.mp4 Download
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