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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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E. V. Flynn More by this author
Publication date:
2006
URN:
uuid:d0fdfc59-a5f5-41d2-aaa0-72921ed57ed7
Local pid:
oai:eprints.maths.ox.ac.uk:247

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