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arXiv · 2412.20968

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

Johannes Anschütz·Arthur-César Le Bras·Lucas Mann
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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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Johannes Anschütz, Arthur-César Le Bras, Lucas Mann. 2024-12-30. A 6-functor formalism for solid quasi-coherent sheaves on the Fargues-Fontaine curve. https://arxiv.org/abs/2412.20968

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