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Six Functors for Pro-Étale Cohomology on v-Stacks

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EHTW04 - Beyond the telescope conjecture

I will present the construction of a 6-functor formalism (joint with Anschütz and Le Bras) for pro-étale $\mathcal O$ and $\mathcal O\flat$-cohomology on small v-stacks. I will then explain how this 6-functor formalism can be used to compute the proétale $\mathcal O\flat$-cohomology of Drinfeld’s upper half space by using an excision sequence. This cohomology appears in a joint “mod p two-towers isomorphism” project currently in progress and has applications to the chromatic splitting conjecture.

This talk is part of the Isaac Newton Institute Seminar Series series.

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