Sullivan's conjecture and applications to arithmetic
Reimagining the Foundations of Algebraic Topology April 07, 2014  April 11, 2014
Location: 60 Evans Halls, UC Berkeley
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
One can phrase interesting objects in terms of fixed points of group actions. For example, class numbers of quadratic extensions of Q can be expressed with fixed points of actions on modular curves. Derived functors are frequently better behaved than their nonderived versions, so it is useful to consider the associated derived functor, called the homotopy fixed points. Sullivan's conjecture is an equivalence between appropriately completed spaces of fixed points and homotopy fixed points for finite pgroups. It was proven independently by H. Miller, G. Carlsson, and J. Lannes. This talk will present Sullivan's conjecture and its solutions, and discuss analogues for absolute Galois groups conjectured by Grothendieck.
Wickelgren.Notes

Download 