Homotopy theory and arithmetic geometry
Connections for Women: Algebraic Topology January 23, 2014  January 24, 2014
Location: SLMath: Eisenbud Auditorium
v1214
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 MorelVoevodsky category for A^1 homotopy theory, and prospaces, 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.
Wickelgren

Download 
v1214
H.264 Video 
v1214.mp4

Download 
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.