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Creators/Authors contains: "Frauke M. Bleher and Ted Chinburg"

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  1. (, arXivorg)
    In this paper we compute cup products of elements of the first étale cohomology group of μℓ over a smooth projective geometrically irreducible curve C over a finite field k when ℓ is a prime and #k≡1 mod ℓ. Over the algebraic closure of k, such products are values of the Weil pairing on the ℓ-torsion of the Jacobian of C. Over k, such cup products are more subtle due to the fact that they naturally take values in Pic(C)⊗Zμ~ℓ rather than in the group μ~ℓ of ℓth roots of unity in k∗. 
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