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

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arxiv 2412.20968 v1 pith:LC7WWSRS submitted 2024-12-30 math.AG math.NT

Johannes Anschütz , Arthur-César Le Bras , Lucas Mann This is my paper
classification math.AGmath.NT
keywords etaleformalismfunctorlocalmathbbpro-adicanalog
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Topological Vector Spaces

    math.AG 2025-09 conditional novelty 6.0 of 10

    A condensed version of the Topological Vector Spaces category is introduced, and fully faithful embeddings from algebraic p-adic vector spaces and from perfect complexes on the Fargues–Fontaine curve are proven.

  2. Categorical K\"unneth formulas for analytic stacks

    math.AG 2025-07 conditional novelty 6.0 of 10

    A categorical Künneth formula is proven for analytic stacks using 6-functor formalisms, yielding new Tannakian reconstruction and p-adic Drinfeld lemma results.

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