Modular varieties of D-elliptic sheaves and the Weil-Deligne bound

Details Modular varieties of D-elliptic sheaves and the Weil-Deligne bound Modular varieties of D-elliptic sheaves and the Weil-Deligne bound

2008-02-12

arxiv.org/abs/0802.1568v1

Mathematics

Number Theory

19 pages; to appear in Crelle

Scientific paper

We compare the asymptotic grows of the number of rational points on modular varieties of D-elliptic sheaves over finite fields to the grows of their Betti numbers as the degree of the level tends to infinity. This is a generalization to higher dimensions of a well-known result for modular curves. As a consequence of the main result, we also produce a new asymptotically optimal sequence of curves.

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