Proves Grothendieck duality for quasi-coherent sheaves on rigid-analytic spaces with dualizing object identified as volume forms, via Ind-Banach spaces.
arXiv preprint arXiv:2603.03012 , year=
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The p-adic monodromy theorem holds for families of G_K-equivariant vector bundles over the Fargues-Fontaine curve parametrized by algebraic-affinoid Q_p-algebras, enabling classification of line bundles without freeness assumptions.
Proves equivalence between smoothness of a rigid analytic variety and smoothness of its nuclear sheaves category in a six-functor formalism, relates compact generation to algebraization, and gives an example of a non-atomically generated internally smooth category.
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Ind-Banach approach to Grothendieck duality in Rigid-analytic geometry
Proves Grothendieck duality for quasi-coherent sheaves on rigid-analytic spaces with dualizing object identified as volume forms, via Ind-Banach spaces.
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The $p$-adic monodromy theorem over algebraic-affinoid algebras
The p-adic monodromy theorem holds for families of G_K-equivariant vector bundles over the Fargues-Fontaine curve parametrized by algebraic-affinoid Q_p-algebras, enabling classification of line bundles without freeness assumptions.
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Smooth categories in a 6 functor formalism and compact generation for nuclear categories in analytic geometry
Proves equivalence between smoothness of a rigid analytic variety and smoothness of its nuclear sheaves category in a six-functor formalism, relates compact generation to algebraization, and gives an example of a non-atomically generated internally smooth category.