Bulletin of the Australian Mathematical Society

Research Article

Descent on Picard groups using functions on curves

Samir Sikseka1

a1 Department of Mathematics, Faculty of Science, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Oman e-mail: siksek@squ.edu.om

Abstract

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 S0004972700020736_inline1 Where S0004972700020736_inline2

We explain how this generalises the usual results on descents on Jacobians and Picard groups of curves.

(Received February 05 2002)