## Abstract

Using Buium's theory of arithmetic differential characters, we construct a filtered F-isocrystal H(A) _{K} associated to an abelian scheme A over a p-adically complete discrete valuation ring with perfect residue field. As a filtered vector space, H(A) _{K} admits a natural map to the usual de Rham cohomology of A, but the Frobenius operator comes from arithmetic differential theory and is not the same as the usual crystalline one. When A is an elliptic curve, we show that H(A) _{K} has a natural integral model H(A), which implies an integral refinement of a result of Buium's on arithmetic differential characters. The weak admissibility of H(A) _{K} depends on the invertibility of an arithmetic-differential modular parameter. Thus the Fontaine functor associates to suitably generic A a local Galois representation of an apparently new kind.

Original language | English |
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Pages (from-to) | 388-428 |

Number of pages | 41 |

Journal | Advances in Mathematics |

Volume | 351 |

DOIs | |

Publication status | Published - 31 Jul 2019 |