Gunnar Carlsson: Free (Z/2Z)^k actions on finite complexes and some problems in etale and motivic homotopy

An interesting conjecture about free actions of 2-tori  T (finite elementary abelian 2-groups) is the the sum of the Betti numbers of the complex being acted upon is greater than 2^{rank T}.  We will show how this problem can be translated into algebraic geometric terms, and then discuss how one might approach the problem with etale or motivic methods.