Functions, reciprocity and the obstruction to divisors on curves
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 0024-6107Full text not available from this repository.
Official URL: http://dx.doi.org/10.1112/jlms/jdn007
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|
|Official Date:||June 2008|
|Number of Pages:||19|
|Page Range:||pp. 789-807|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC), Seventh Framework Programme (European Commission) (FP7)|
1. N. Bruin and M. Stoll, ‘Deciding existence of rational points on curves: an experiment’, Experiment.
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