Poincaré biextension and ideles on an algebraic curve
نویسنده
چکیده
Arbarello, de Concini, and Kac have constructed a central extension of the ideles group on a smooth projective algebraic curve C. We show that this central extension induces the theta-bundle on the class group of degree g−1 divisors on C, where g is the genus of the curve C. The other result of the paper is the relation between the product of the norms of the tame symbols over all points of the curve, considered as a pairing on the ideles group, and the Poincaré biextension of the Jacobian of C. As an application we get a new proof of the adelic formula for the Weil pairing.
منابع مشابه
Poincaré biextension and idèles on the algebraic curve
The Weil pairing of two element from the torsion of the Jacobian of an algebraic curve may be given by a product of local Hilbert symbols of two special idèles associated to the torsion elements of the Jacobian. On the other hand Arbarello, de Concini and Kac have constructed some central extension of the group of idèles on an algebraic curve, in which the commutator is also equal up to sign to...
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تاریخ انتشار 2007