On an analogue of the conjecture of Birch and Swinnerton-Dyer for Abelian schemes over higher dimensional bases over finite fields
نویسنده
چکیده
We formulate an analogue of the conjecture of Birch and Swinnerton-Dyer for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields. We prove some conditional results for the p′-part on it, and prove the p′-part of the conjecture for constant or isoconstant Abelian schemes, in particular the p′-part for (1) relative elliptic curves with good reduction or (2) Abelian schemes with constant isomorphism type of A [p] or (3) Abelian schemes with supersingular generic fibre over products of curves, Abelian varieties and K3 surfaces, and the full conjecture for relative elliptic curves with good reduction over curves and for constant Abelian schemes over arbitrary bases.
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