Develops Tate-Sen formalism for Galois representations over convergent de Rham period ring, proving cohomology finiteness under non-Liouville Sen weights and category equivalence for algebraic weights.
p -adic H odge theory for rigid-analytic varieties
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Proves independence of locally analytic vectors from G and G_b actions in dual infinite-level local Shimura varieties and deduces commutation properties for the p-adic Jacquet-Langlands functor plus isomorphism of de Rham cohomologies.
Computes the geometric Sen operator on arbitrary Shimura varieties via equivariant bundles and the Hodge-Tate period map, yielding rational vanishing of completed cohomology.
Defines rational analytic syntomification X^Syn for rigid-analytic varieties over Q_p, establishes Poincaré duality and Chern classes, identifies its vector bundles with de Rham bundles on the Fargues-Fontaine curve, and recovers classical p-adic Hodge comparisons.
citing papers explorer
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Galois representations over convergent de Rham period ring
Develops Tate-Sen formalism for Galois representations over convergent de Rham period ring, proving cohomology finiteness under non-Liouville Sen weights and category equivalence for algebraic weights.
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A Jacquet-Langlands functor for $p$-adic locally analytic representations
Proves independence of locally analytic vectors from G and G_b actions in dual infinite-level local Shimura varieties and deduces commutation properties for the p-adic Jacquet-Langlands functor plus isomorphism of de Rham cohomologies.
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Locally analytic completed cohomology
Computes the geometric Sen operator on arbitrary Shimura varieties via equivariant bundles and the Hodge-Tate period map, yielding rational vanishing of completed cohomology.
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Rational analytic syntomic cohomology
Defines rational analytic syntomification X^Syn for rigid-analytic varieties over Q_p, establishes Poincaré duality and Chern classes, identifies its vector bundles with de Rham bundles on the Fargues-Fontaine curve, and recovers classical p-adic Hodge comparisons.