Finding large Selmer rank via an arithmetic theory of local constants
| dc.creator | Mazur, Barry | |
| dc.creator | Rubin, Karl | |
| dc.date | 2005-12-05 | |
| dc.date | 2006-09-02 | |
| dc.date.accessioned | 2026-07-07T06:54:50Z | |
| dc.date.available | 2026-07-07T06:54:50Z | |
| dc.description | We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields. Suppose $K/k$ is a quadratic extension of number fields, $E$ is an elliptic curve defined over $k$, and $p$ is an odd prime. Let $F$ denote the maximal abelian $p$-extension of $K$ that is unramified at all primes where $E$ has bad reduction and that is Galois over $k$ with dihedral Galois group (i.e., the generator $c$ of $Gal(K/k)$ acts on $Gal(F/K)$ by -1). We prove (under mild hypotheses on $p$) that if the rank of the pro-$p$ Selmer group $S_p(E/K)$ is odd, then the rank of $S_p(E/L)$ is at least $[L:K]$ for every finite extension $L$ of $K$ in $F$. | |
| dc.description | Revised and improved. To appear in Annals of Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0512085 | |
| dc.identifier | http://arxiv.org/abs/math/0512085 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106082 | |
| dc.subject | Number Theory | |
| dc.subject | 11G05, 11R20 (Primary) 11G10, 11R23, 14G05 (Secondary) | |
| dc.title | Finding large Selmer rank via an arithmetic theory of local constants | |
| dc.type | text |