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SUMMARY:Minimal weights of mod p Galois representations - Hanneke Wiersema
  (King's College London)
DTSTART:20201110T143000Z
DTEND:20201110T153000Z
UID:TALK152761@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:The strong form of Serre's conjecture states that every two-di
 mensional continuous\, odd\, irreducible mod p representation of the absol
 ute Galois group of Q arises from a modular form of a specific minimal wei
 ght\, level and character. In this talk we use modular representation theo
 ry to prove the minimal weight is equal to a notion of minimal weight insp
 ired by work of Buzzard\, Diamond and Jarvis. Moreover\, using the Breuil-
 Mézard conjecture we give a third interpretation of this minimal weight a
 s the smallest k>1 such that the representation has a crystalline lift of 
 Hodge-Tate type (0\, k-1). Finally\, we will report on work in progress wh
 ere we study similar questions in the more general setting of mod p Galois
  representations over a totally real field.\n\nIf you like to attend the t
 alk\, please register here using your full professional name: maths-cam-ac
 -uk.zoom.us/meeting/register/tJIod-Chrz4tHNQn2wfLpMF9aZoMjDJDmvF3
LOCATION:Online
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