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Minimal weights of mod p Galois representations

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  • UserHanneke Wiersema (King's College London)
  • ClockTuesday 10 November 2020, 14:30-15:30
  • HouseOnline.

If you have a question about this talk, please contact Rong Zhou.

The strong form of Serre’s conjecture states that every two-dimensional continuous, odd, irreducible mod p representation of the absolute Galois group of Q arises from a modular form of a specific minimal 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 Breuil-M├ęzard conjecture we give a third interpretation of this minimal weight as 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 where we study similar questions in the more general setting of mod p Galois representations over a totally real field.

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This talk is part of the Number Theory Seminar series.

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