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Exhibiting SHA[2] on hyperelliptic Jacobians

Abstract:

We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves, with an emphasis on the theory and practice of visualisation. Especially for hyperelliptic curves, this often enables the computation of ranks of Jacobians, even when the 2-Selmer bound does not bound the rank sharply. This was previously only possible for a few special cases. For curves of genus 2, we also demonstrate a connection with degree 4 del Pezzo surfaces, and show how the Brauer-Man...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher version

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Publisher copy:
10.1016/j.jnt.2005.10.007

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Publisher:
Elsevier Publisher's website
Journal:
Journal of Number Theory Journal website
Volume:
118
Issue:
2
Pages:
266-291
Publication date:
2006-06-05
DOI:
ISSN:
0022-314X
URN:
uuid:2f8e607e-4f8a-4e22-9ff0-3a1b215be8ae
Source identifiers:
148108
Local pid:
pubs:148108

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