Delta isocrystal and crystalline cohomology of abelian schemes

Abstract: Given an abelian scheme A over a p-adic ring, using the theory of arithmetic jets of A, one can associate a filtered F-isocrystal, which is referred to as the delta isocrystal associated with A. The delta isocrystal admits a natural map to the Hodge sequence of the first de Rham cohomology of A. Recently, we have shown that the Frobenius operator on the delta isocrystal is compatible with the crystalline Frobenius operator on the de Rham cohomology (under the de Rham-crystalline comparison isomorphism). This allows us to derive a comparison result between the delta isocrystal and the crystalline cohomology of abelian schemes in the category of filtered F-isocrystals. This talk is partly based on joint work with Lance Gurney and Arnab Saha.

number theory

Audience: researchers in the topic

London number theory seminar

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