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Frobenius elements in Galois representations with SL_n image

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Pages (from-to)165-171
JournalJournal of Number Theory
Volume188
Early online date19 Feb 2018
DOIs
Accepted/In press17 Jan 2018
E-pub ahead of print19 Feb 2018
PublishedJul 2018

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Abstract

Suppose we have a elliptic curve over a number field whose mod
$l$ representation has image isomorphic to $SL_2(\mathbb{F}_l)$. We
present a method to determine Frobenius elements of the associated Galois
group which incorporates the linear structure available. We are able to
distinguish $SL_n(\mathbb{F}_l)$-conjugacy from $GL_n(\mathbb{F}_l)$-
conjugacy; this can be thought of as being analogous to a result which
distinguishes $A_n$-conjugacy from $S_n$-conjugacy when the Galois group
is considered as a permutation group.

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