We prove a level raising mod theorem for elliptic curves over. It generalizes theorems of Ribet and Diamond-Taylor and also explains different sign phenomena compared to odd. We use it to study the 2-Selmer groups of modular abelian varieties with common modÂ 2 Galois representation. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families.
|Original language||English (US)|
|Number of pages||33|
|State||Published - Aug 1 2016|
- Selmer groups
- modular forms
ASJC Scopus subject areas
- Algebra and Number Theory