Alex Waugh
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PDL C-401
Title: Ghosts hiding in the Frobenius
Abstract: In characteristic p, we often have the freshman's dream: (x+y)^p = x^p + y^p. In commutative algebra, this is an absolute equality. That is, the equality sign means equality on the nose. In this talk, I will discuss a derived/homotopical perspective on this dream, where equality is replaced with "homotopic". By keeping track of all of the resulting homotopical data, I will show how to produce maps which were hidden within the derived Frobenius and produce operations which will act on Hopf algebra cohomology. Time permitting, I will connect this construction with the vanishing of certain Tate cohomology and operad theory.