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SUMMARY:Pedro Lemos (University College London)
DTSTART:20201111T160000Z
DTEND:20201111T170000Z
DTSTAMP:20260423T022812Z
UID:hnts/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/13/">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 Heilbronn number theory seminar\n\n\nAbstract\nDue to the work 
 of several mathematicians\, it is known that if p is a prime >37\, then th
 e image of the residual Galois representation $\\bar{\\rho}_{E\,p}: G_{\\m
 athbb{Q}}\\rightarrow {\\rm GL}_2(\\mathbb{F}_p)$ attached to an elliptic 
 curve $E/\\mathbb{Q}$ without complex multiplication is either ${\\rm GL}_
 2(\\mathbb{F}_p)$\, or is contained in the normaliser of a non-split Carta
 n subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$. I will report on a recent join
 t work with Samuel Le Fourn\, where we improve this result (at least for l
 arge enough primes) 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 n
 on-split Cartan subgroup of ${\\rm GL}_2(\\mathbb{F}_p)$.\n
LOCATION:https://researchseminars.org/talk/hnts/13/
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