Symmetric powers and the étale Dold-Thom theorem

Algebra Seminar
Monday, August 31, 2015 - 15:00
1 hour (actually 50 minutes)
Skiles 006
Stanford University
After reminding everyone why the symmetric powers Sym^n X of a scheme arise and are interesting from the point of view of the Weil conjectures, I'll recall the Dold-Thom theorem of algebraic topology, which governs the behavior of symmetric powers of a topological space. I'll then explain how the notion of étale homotopy allows us to compare these two realms of arithmetic geometry and algebraic topology, providing a homotopical refinement of a small part of the Weil conjectures.