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Tannaka duality and 1-affineness

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arxiv 2311.04515 v1 pith:S6SY5BVC submitted 2023-11-08 math.AG math.ATmath.CT

Germán Stefanich This is my paper · ORCID
classification math.AGmath.ATmath.CT
keywords affinenesscategoriesdualitysheavestannakaappliedconsequencededuce
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We show that Lurie's results on Tannaka duality for geometric stacks hold without any tameness hypotheses. We deduce this as a consequence of an affineness theorem in the theory of sheaves of categories. This affineness result is also applied to the study of tensor product and integral transform formulas for categories of quasicoherent sheaves.

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  1. An axiomatic approach to analytic $1$-affineness

    math.AG 2025-09 conditional novelty 6.0 of 10

    An axiomatic framework proves 1-affineness for analytic Betti stacks, analytic de Rham stacks, and rigid analytic varieties, giving categorical Künneth formulas.

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