A 6-functor formalism for solid quasi-coherent sheaves on the Fargues-Fontaine curve

Abstract

We develop a 6-functor formalism ${\mathcal{D}}_{[0,\infty )}(-)$ with ${\mathbb{Z}}_p$-linear coefficients on small v-stacks, and discuss consequences for duality and finiteness for pro-étale cohomology of rigid-analytic varieties of general pro-étale ${\mathbb{Q}}_p$-local systems as well as first examples motivated by a potential $p$-adic analog of Fargues-Scholze's geometrization program of the local Langlands correspondence.

85 pages. Changes after referee report; version for publication