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ON THE EULER CHARACTERISTICS OF SIGNED SELMER GROUPS

Published online by Cambridge University Press:  09 July 2019

SUMAN AHMED
Affiliation:
School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China email npur.suman@gmail.com
MENG FAI LIM*
Affiliation:
School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, PR China email limmf@mail.ccnu.edu.cn

Abstract

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

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

M. F. Lim is supported by the National Natural Science Foundation of China under Grant Nos. 11550110172 and 11771164.

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