English

Large Selmer groups over number fields

Number Theory 2015-10-12 v4 Representation Theory

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.

Keywords

Cite

@article{arxiv.0805.1231,
  title  = {Large Selmer groups over number fields},
  author = {Alex Bartel},
  journal= {arXiv preprint arXiv:0805.1231},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-21T10:38:44.105Z