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Lucas Mann: A p-adic six functor formalism in rigid analytic geometry, III
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https://m.youtube.com/watch?v=MwWqysSnY5k Abstract: Using Clausen--Scholze's condensed mathematics, we introduce a full 6-functor formalism for the p-adic cohomology on rigid-analytic varieties over p-adic fields, and more generally on Scholze's diamonds and v-stacks. The idea is to embed étale F_p-sheaves on a v-stack X into a certain category of "solid quasicoherent almost O_X^+/p-modules" and construct the six functors for the latter category. As an application we prove Poincaré duality for p-adic cohomology on rigid varieties and in joint work with Hansen obtain new results on the p-adic Jacquet-Langlands functor. Moreover, in ongoing joint work with Anschütz and Le Bras we construct a similar 6-functor formalism for pro-étale Q_p-cohomology with the aim of reproving and extending previous duality results of Colmez-Gilles-Niziol
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