On the Euler characteristics of signed Selmer groups

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.

arXiv comment9 pages

References in corpus (1)

• On Selmer groups in the supersingular reduction case

Cited by in corpus (4)

• On Selmer groups in the supersingular reduction case
• On the cohomology of Kobayashi's plus/minus norm groups and applications
• Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above p
• On the cohomology of plus/minus Selmer groups of supersingular elliptic curves in weakly ramified base fields