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

Mihran Papikian

doi:10.1515/CRELLE.2009.004

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

Mihran Papikian

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 produce a new asymptotically optimal sequence of curves.

Original language	English (US)
Pages (from-to)	115-134
Number of pages	20
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	626
DOIs	https://doi.org/10.1515/CRELLE.2009.004
State	Published - Jan 2009

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1515/CRELLE.2009.004

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abstract = "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 produce a new asymptotically optimal sequence of curves.",

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AB - 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 produce a new asymptotically optimal sequence of curves.

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

Abstract

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