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Homotopy theory and arithmetic geometry

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

January 23, 2014 (10:45 AM PST - 11:45 AM PST)
Speaker(s): Kirsten Wickelgren (Georgia Institute of Technology)
Location: MSRI: Simons Auditorium


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.

19845?type=thumb Wickelgren 115 KB application/pdf Download
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