Large Selmer groups over number fields

Abstract

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.

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

References in corpus (2)

• Regulator constants and the parity conjecture
• Period, index and potential sha

Cited by in corpus (5)

• Index formulae for integral Galois modules
• $p$-Selmer growth in extensions of degree $p$
• On Brauer-Kuroda type relations of S-class numbers in dihedral extensions
• Elliptic curves with p-Selmer growth for all p
• On a BSD-type formula for L-values of Artin twists of elliptic curves