Mathematics – Number Theory
Scientific paper
2011-04-12
Mathematics
Number Theory
21 pages
Scientific paper
Let $E$ be an elliptic curve over $\mathbb{Q}$ with good supersingular reduction at a prime $p\geq 3$ and $a_p=0$. We generalise the definition of Kobayashi's plus/minus Selmer groups over $\mathbb{Q}(\mu_{p^\infty})$ to $p$-adic Lie extensions $K_\infty$ of $\mathbb{Q}$ containing $\mathbb{Q}(\mu_{p^\infty})$, using the theory of $(\phi,\Gamma)$-modules and Berger's comparison isomorphisms. We show that these Selmer groups can be equally described using the "jumping conditions" of Kobayashi via the theory of overconvergent power series. Moreover, we show that such an approach gives the usual Selmer groups in the ordinary case.
Lei Antonio
Zerbes Sarah Livia
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