Galois symmetries of the stable homology of integer symplectic groups


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October 22, 2020 4:30 pm - 5:30 pm
via Zoom Video Conferencing

Akshay Venkatesh - Institute for Advanced Study

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 carries an extra structure -- an action of the Galois group of K --  which is arithmetically interesting.

In joint work with Feng and Galatius, we compute this action (or rather a slight variant) in the case of the moduli space of abelian varieties. I will explain the answer and why I find it interesting. No familiarity with abelian varieties will be assumed -- I will emphasize topology over algebraic geometry.