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CATEGORIES:Number Theory Seminar
SUMMARY:Minimal weights of mod p Galois representations -
Hanneke Wiersema (King's College London)
DTSTART;TZID=Europe/London:20201110T143000
DTEND;TZID=Europe/London:20201110T153000
UID:TALK152761AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/152761
DESCRIPTION:The strong form of Serre's conjecture states that
every two-dimensional continuous\, odd\, irreducib
le mod p representation of the absolute Galois gro
up of Q arises from a modular form of a specific m
inimal weight\, level and character. In this talk
we use modular representation theory to prove the
minimal weight is equal to a notion of minimal wei
ght inspired by work of Buzzard\, Diamond and Jarv
is. Moreover\, using the Breuil-Mézard conjecture
we give a third interpretation of this minimal wei
ght as the smallest k>1 such that the representati
on has a crystalline lift of Hodge-Tate type (0\,
k-1). Finally\, we will report on work in progress
where we study similar questions in the more gene
ral setting of mod p Galois representations over a
totally real field.\n\nIf you like to attend the
talk\, please register here using your full profes
sional name: maths-cam-ac-uk.zoom.us/meeting/regis
ter/tJIod-Chrz4tHNQn2wfLpMF9aZoMjDJDmvF3
LOCATION:Online
CONTACT:Rong Zhou
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