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math.NT2026
Reduction modulo p of crystalline Galois representations via μ_p-equivariance
Bhargav Bhatt, Toby Gee, Mark Kisin
For a crystalline representation of the absolute Galois group of Q_p, with given Hodge-Tate weights, we obtain new constraints on the inertial weights of its mod p reduction. This…
math.NT2026
Prescribed lifts of 2-dimensional representations
Matthew Emerton, Toby Gee, Lue Pan +1
Let F be a totally real field, and let p be prime. Under standard Taylor--Wiles hypotheses, we show that an irreducible, 2-dimensional, totally odd mod p representation of the abso…
math.NT2026
A categorical p-adic Langlands correspondence for GL_2(Q_p)
Andrea Dotto, Matthew Emerton, Toby Gee
Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a d…