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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the modularity of elliptic curves over imaginar
y quadratic fields - Ana Caraiani (Imperial Colleg
e London)
DTSTART;TZID=Europe/London:20220620T133000
DTEND;TZID=Europe/London:20220620T143000
UID:TALK174401AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/174401
DESCRIPTION:I will survey how to prove the modularity of ellip
tic curves defined over the rational numbers\, as
pioneered by Wiles and Taylor-Wiles and completed
by Breuil\, Conrad\, Diamond and Taylor. I will al
so mention the case of elliptic curves defined ove
r real quadratic fields\, more recently completed
by Freitas\, Le Hung and Siksek. I will then expla
in why the case of imaginary quadratic fields is q
ualitatively different from the previous ones. Fin
ally\, I will discuss joint work in progress with
James Newton\, where we prove a local-global compa
tibility result in the crystalline case for Galois
representations attached to torsion classes occur
ring in the cohomology of locally symmetric spaces
. This has an application to the modularity of ell
iptic curves over imaginary quadratic fields\, whi
ch also builds on recent work of Allen\, Khare and
Thorne. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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