4:00–5:00 pm
Ryerson Physical Laboratory, Room 251
1100 East 58th Street
Chicago, IL 60637
Abstract: There are many natural sequences of moduli spaces in algebraic geometry whose homology approaches a "limit" despite the fact that the spaces themselves have growing dimension. If these moduli spaces are defined over a field \(K\), this limiting homology comes with an extra structure -- an action of the Galois group of \(K\) -- and to understand this extra structure is often of arithmetic interest. First of all I'll introduce a few examples of this situation. Then I will specialize to the case of the moduli space of abelian varieties: I will explain the answer, why it is interesting, and some geometric consequences. No familiarity with abelian varieties will be assumed for the talk. This is joint work with Tony Feng and Soren Galatius.