A categorical Künneth formula is proven for analytic stacks using 6-functor formalisms, yielding new Tannakian reconstruction and p-adic Drinfeld lemma results.
A 6-functor formalism for solid quasi-coherent sheaves on the Fargues-Fontaine curve
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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-\'etale cohomology of rigid-analytic varieties of general pro-\'etale $\mathbb{Q}_p$-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.
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Categorical K\"unneth formulas for analytic stacks
A categorical Künneth formula is proven for analytic stacks using 6-functor formalisms, yielding new Tannakian reconstruction and p-adic Drinfeld lemma results.