Bright, M. (Martin) and Siksek, Samir. (2008) Functions, reciprocity and the obstruction to divisors on curves. Journal of the London Mathematical Society, Vol.77 (Pt.3). pp. 789-807. ISSN 0024-6107

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Abstract

Let k be a number field, X a smooth curve over k, and f a non-constant element of the function field k(X). If v is a prime of k then denote the completion of k at v by k(v), and let X-v := X x k(v). In this paper, we introduce an abelian extension Ilk, depending on f in a natural way, which we call the class field of k belonging to f. We give an explicit homomorphism Pi Pic(X-v) -> Gal(l/k) such that the image of Pic(X) in Pi Pic(X-v) is in the kernel of this map. We explain how this can often obstruct the existence of k-rational divisors of certain degrees.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Divisor theory, Curves, Algebraic, Functions, Reciprocity theorems
Journal or Publication Title:	Journal of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6107
Date:	June 2008
Volume:	Vol.77
Number:	Pt.3
Number of Pages:	19
Page Range:	pp. 789-807
Identification Number:	10.1112/jlms/jdn007
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Seventh Framework Programme (European Commission) (FP7)
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URI:	http://wrap.warwick.ac.uk/id/eprint/29875

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