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arXiv · 1905.11038

On the Euler characteristics of signed Selmer groups

Suman Ahmed·Meng Fai Lim
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Abstract

Let $p$ be an odd prime number, and $E$ an elliptic curve defined over a number field with good reduction at every prime of $F$ above $p$. In this short note, we compute the Euler characteristics of the signed Selmer groups of $E$ over the cyclotomic $\Zp$-extension. The novelty of our result is that we allow the elliptic curve to have mixed reduction types for primes above $p$ and that we allow mixed signs in the definition of the signed Selmer groups.

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Suman Ahmed, Meng Fai Lim. 2019-05-27. On the Euler characteristics of signed Selmer groups. https://doi.org/10.1017/s0004972719000704

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