The Mathematical Institute, University of Oxford, Eprints Archive

The Brauer-Manin Obstruction and Sha[2].

Bright, M.J. and Bruin, N. and Flynn, E. V. and Logan, A. (2007) The Brauer-Manin Obstruction and Sha[2]. LMS Journal of Computation and Mathematics, 10 . pp. 354-377. ISSN 1461-1570

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Official URL: http://www.lms.ac.uk/jcm/

Abstract

We discuss the Brauer-Manin obstruction on del Pezzo surfaces of degree 4. We outline a detailed algorithm for computing the obstruction and provide associated programs in magma. This is illustrated with the computation of an example with an irreducible cubic factor in the singular locus of the defining pencil of quadrics (in contrast to previous examples, which had at worst quadratic irreducible factors). We exploit the relationship with the Tate-Shafarevich group to give new types of examples of Sha[2], for families of curves of genus 2 of the form y^2 = f(x), where f(x) is a quintic containing an irreducible cubic factor.

Item Type:Article
Subjects:H - N > Number theory
Research Groups:Number Theory Group
ID Code:797
Deposited By:E. Victor Flynn
Deposited On:01 Sep 2009 08:35
Last Modified:01 Sep 2009 08:35

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