Congruence Relation

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Jean-stefan Koskivirta - One of the best experts on this subject based on the ideXlab platform.

  • Congruence Relations for Shimura Varieties Associated with $GU(n-1,1)$
    Canadian Journal of Mathematics, 2014
    Co-Authors: Jean-stefan Koskivirta
    Abstract:

    AbstractWe prove the Congruence Relation for the mod–preduction of Shimura varieties associated with a unitary similitude groupGU(n– 1, 1) over ℚ whenpis inert andnodd. The case whennis even was obtained by T. Wedhorn and O. Bültel, as a special case of a result of B. Moonen, when theμ–ordinary locus of thep–isogeny space is dense. This condition fails in our case. We show that every supersingular irreducible component of the special fiber of p–ℐsog is annihilated by a degree one polynomial in the Frobenius elementF, which implies the Congruence Relation.

  • Congruence Relations for Shimura Varieties Associated with GU (n − 1, 1)
    Canadian Journal of Mathematics, 2014
    Co-Authors: Jean-stefan Koskivirta
    Abstract:

    We prove the Congruence Relation for the mod-p reduction of Shimura varieties associated with a unitary similitude group GU (n − 1, 1) over Q when p is inert and n odd. The case when n is even was obtained by T. Wedhorn and O. Bültel , as a special case of a result of B. Moonen, when the µ-ordinary locus of the p-isogeny space is dense. This condition fails in our case. We show that every supersingular irreducible component of the special fiber of p-Isog is annihilated by a degree one polynomial in the Frobenius element F, which implies the Congruence Relation.

Roohallah Daneshpayeh - One of the best experts on this subject based on the ideXlab platform.

Ming Ping-hua - One of the best experts on this subject based on the ideXlab platform.

Akbar Rezaei - One of the best experts on this subject based on the ideXlab platform.

Li Ai-ping - One of the best experts on this subject based on the ideXlab platform.