Large Selmer groups over number fields
Identifieur interne : 000481 ( Main/Exploration ); précédent : 000480; suivant : 000482Large Selmer groups over number fields
Auteurs : Alex Bartel [Royaume-Uni]Source :
- Mathematical Proceedings of the Cambridge Philosophical Society [ 0305-0041 ] ; 2010-01.
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.
Url:
DOI: 10.1017/S0305004109990132
Affiliations:
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<front><div type="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.</div>
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