Mittagsseminar: Lucas Mann (Bonn): p-Adic Six Functors in Rigid-Analytic Geometry II
Tuesday, 19.10.2021 10:15 im Raum SRZ 216/217
Motivated by p-adic Poincaré duality in rigid-analytic geometry, we develop a p-adic six functor formalism on rigid-analytic varieties, or more generally diamonds. This is achieved by defining a category of "quasi-coherent $O_X^+/p$-modules" on a diamond $X$ and then using the recent development of a quasi-coherent 6-functor formalism on schemes by Clausen-Scholze to obtain a similar 6-functor formalism on diamonds. One easily deduces the desired p-adic Poincaré duality on a smooth proper rigid variety $X$ in mixed characteristic, noting that by Scholze's primitive comparison theorem, $\mathbb F_p$-cohomology on $X$ can be computed via cohomology of the sheaf $O_X^+/p$. Of course our p-adic 6-functor formalism allows for many more potential applications, for example we expect to gain new insights into the p-adic Langlands program.