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arXiv · 0805.1231

Large Selmer groups over number fields

Alex Bartel
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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.

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Alex Bartel. 2009-06-24. Large Selmer groups over number fields. https://doi.org/10.1017/s0305004109990132

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