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SUMMARY:Pedro Lemos (University College London)
DTSTART:20201216T160000Z
DTEND:20201216T170000Z
DTSTAMP:20260418T063529Z
UID:LNTS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/21/">Re
 sidual Galois representations of elliptic curves with image in the normali
 ser of a non-split Cartan</a>\nby Pedro Lemos (University College London) 
 as part of London number theory seminar\n\n\nAbstract\nIt is known that if
  $p$ is a prime $>37$\, then the image of the residual Galois representati
 on $\\bar{\\rho}_{E\,p}: G_{\\mathbb{Q}}\\rightarrow {\\rm GL}_2(\\mathbb{
 F}_p)$ attached to an elliptic curve $E/\\mathbb{Q}$ without complex multi
 plication is either ${\\rm GL}_2(\\mathbb{F}_p)$\, or is contained in the 
 normaliser of a non-split Cartan subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$.
  I will report on a recent joint work with Samuel Le Fourn where we improv
 e this result by showing that if $p>1.4\\times 10^7$\, then $\\bar{\\rho}_
 {E\,p}$ is either surjective\, or its image is the normaliser of a non-spl
 it Cartan subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$.\n
LOCATION:https://researchseminars.org/talk/LNTS/21/
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