Cohen-Macaulayness up to finite covers

Cohen-Macaulayness up to finite covers

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Bhargav Bhatt, University of Michigan

Zoom link:  https://princeton.zoom.us/j/91248028438

A fundamental theorem in F-singularity theory (due to Hochster-Huneke) is that obstructions to Cohen-Macaulayness of a variety in positive characteristic (e.g., certain cohomology groups) can be annihilated by passing to finite covers, unlike in characteristic 0. This talk will be dedicated to the mixed characteristic analog of this result. I'll discuss the statement, consequences for vanishing theorems, and one of the two primary inputs to the proof (joint work with Lurie): a Riemann-Hilbert functor that attaches coherent objects to constructible F_p-sheaves on algebraic varieties in characteristic 0 and interacts well with the perverse t-structure.