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Large Selmer groups over number fields

Published online by Cambridge University Press:  15 July 2009

ALEX BARTEL
ALEX BARTEL*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilber force Road, Cambridge, CB3 0WB. e-mail: ac528@cam.ac.uk
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Abstract

Let p be a prime number and M a quadratic number field, M ≠ ℚ() if p ≡ 1 mod 4. We will prove that for any positive integer d there exists a Galois extension F/ℚ with Galois group D2p and an elliptic curve E/ℚ such that F contains M and the p-Selmer group of E/F has size at least pd.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 1 , January 2010 , pp. 73 - 86
Copyright
Copyright © Cambridge Philosophical Society 2009

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