a1 Department of Mathematics, Faculty of Science, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Oman e-mail: [email protected]
Let k be a perfect field, X a smooth curve over k, and denote by Xc the subset of closed points of X. We show that for any non-constant element f of the function field k (X) there exists a natural homomorphism Where
We explain how this generalises the usual results on descents on Jacobians and Picard groups of curves.
(Received February 05 2002)