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.
Sur certains types de repr\'esentations p -adiques du groupe de G alois d'un corps local;\ construction d'un anneau de B arsotti- T ate
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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.
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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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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.