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SUMMARY:Hanneke Wiersema (King's College London)
DTSTART:20201110T143000Z
DTEND:20201110T153000Z
DTSTAMP:20260421T153040Z
UID:CamNT/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CamNT/6/">Mi
 nimal weights of mod p Galois representations</a>\nby Hanneke Wiersema (Ki
 ng's College London) as part of Cambridge Number Theory Seminar\n\n\nAbstr
 act\nThe strong form of Serre's conjecture states that every two-dimension
 al continuous\, odd\, irreducible mod p representation of the absolute Gal
 ois group of $\\mathbb{Q}$ arises from a modular form of a specific minima
 l weight\, level and character. In this talk we use modular representation
  theory to prove the minimal weight is equal to a notion of minimal weight
  inspired by work of Buzzard\, Diamond and Jarvis. Moreover\, using the Br
 euil-Mézard conjecture we give a third interpretation of this minimal wei
 ght as the smallest k>1 such that the representation has a crystalline lif
 t of Hodge-Tate type $(0\, k-1)$. Finally\, we will report on work in prog
 ress where we study similar questions in the more general setting of mod $
 p$ Galois representations over a totally real field.\n
LOCATION:https://researchseminars.org/talk/CamNT/6/
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