Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic \(\mathcal D\)-modules

DOI10.4171/RSMUP/131-7zbMath1327.14101arXiv1105.5796MaRDI QIDQ396490

Tomoyuki Abe

Publication date: 13 August 2014

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5796

zbMATH Keywords

\(p\)-adic cohomologyrigid cohomologyarithmetic \(\mathcal D\)-module

Mathematics Subject Classification ID

Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) (p)-adic cohomology, crystalline cohomology (14F30) (p)-adic differential equations (12H25)

Related Items (11)

Langlands correspondence for isocrystals and the existence of crystalline companions for curves ⋮ Lagrangianity for log extendable overconvergent \(F\)-isocrystals ⋮ Generalized hypergeometric arithmetic 𝒟-modules under a 𝓅-adic non-Liouvilleness condition ⋮ La surcohérence entraîne l'holonomie ⋮ Langlands program for \(p\)-adic coefficients and the petits camarades conjecture ⋮ AROUND THE NEARBY CYCLE FUNCTOR FOR ARITHMETIC -MODULES ⋮ Drinfeld's lemma for F-isocrystals, II: Tannakian approach ⋮ On Beilinson's equivalence for \(p\)-adic cohomology ⋮ BETTI NUMBER ESTIMATES IN -ADIC COHOMOLOGY ⋮ On stability of \(\mathcal{D}\)-modules under tensor product of complex ⋮ Bessel \(F\)-isocrystals for reductive groups

Cites Work

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• Coherence of certain overconvergent isocrystals without Frobenius structures on curves
• Finiteness of the homological dimension of weakly complete algebras of differential operator with overconvergent coefficients
• Gauss sums and the p-adic \(\Gamma\)-function
• Explicit Frobenius descent for \({\mathcal D}^\dagger\)-modules
• Grothendieck duality and base change
• Finiteness of rigid cohomology with coefficients
• On the compability of the Frobenius isomorphism with relative duality
• Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
• ${\cal D}$-modules arithmétiques. II: Descente par Frobenius
• Dualité locale et holonomie pour les ${\cal D}$-modules arithmétiques
• Product formula forp-adic epsilon factors

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