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arXiv · 1606.03618

Number of irreducible mod l rank 2 sheaves on curves over finite fields

Gebhard Böckle·Chandrashekhar Khare
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Abstract

Let X be a smooth projective curve of genus g over a finite field F_q of characteristic p. Consider primes l different from p. We formulate some questions related to a well known counting formula of Drinfeld. Drinfeld counts rank 2, irreducible l-adic sheaves on the base change X_n of X to F_{q^n} as n varies. We would like to count rank 2, irreducible mod l sheaves on X_n as n varies. Drinfeld's l-adic count gives an upper bound for the mod l count. We conjecture that Drinfeld's count is the correct asymptotic for the count of rank 2, irreducible mod l sheaves on X_n as n varies with (n,\ell)=1.

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Gebhard Böckle, Chandrashekhar Khare. 2016-06-11. Number of irreducible mod l rank 2 sheaves on curves over finite fields. https://arxiv.org/abs/1606.03618

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