Large Selmer groups over number fields

Details Large Selmer groups over number fields Large Selmer groups over number fields

2008-05-09

arxiv.org/abs/0805.1231v4

Math. Proc. Cambridge Philos. Soc. (2010), 148, 73-86

Mathematics

Number Theory

15 pages, final version, to appear in Math. Proc. Cambridge Philos. Soc

Scientific paper

Let p be a prime number and M a quadratic number field, M not equal to
Q(\sqrt{p}) if p is congruent to 1 modulo 4. We will prove that for any
positive integer d there exists a Galois extension F/Q with Galois group D_{2p}
and an elliptic curve E/Q such that F contains M and the p-Selmer group of E/F
has size at least p^d.

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