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2 results

  • Stabilité de l’holonomie sur les variétés quasi-projectives

  • Part of
  • Daniel Caro
  • Journal:
    Compositio Mathematica / Volume 147 / Issue 6 / November 2011
    Published online by Cambridge University Press:
    24 August 2011, pp. 1772-1792
    Print publication:
    November 2011
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  • Let 𝒱 be a mixed characteristic complete discrete valuation ring with perfect residue field k. We solve Berthelot’s conjectures on the stability of the holonomicity over smooth projective formal 𝒱-schemes. Then we build a category of F-complexes of arithmetic 𝒟-modules over quasi-projective k-varieties with bounded and holonomic cohomology. We obtain its stability under Grothendieck’s six operations.

  • Comparison between Swan conductors and characteristic cycles

  • Part of
  • Tomoyuki Abe
  • Journal:
    Compositio Mathematica / Volume 146 / Issue 3 / May 2010
    Published online by Cambridge University Press:
    10 March 2010, pp. 638-682
    Print publication:
    May 2010
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  • In this paper, we define Swan conductors for unit-root overconvergent F-isocrystals using the theory of arithmetic 𝒟-modules due to Berthelot. Our Swan conductors are compared with the Swan conductors for ℓ-adic sheaves constructed by Kato and Saito using a geometric method. As an application, we prove the integrality of Swan conductors in the sense of Kato and Saito under the ‘resolution of singularities’ assumption.