5 papers
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…
The Breuil-Mézard conjecture for potentially Barsotti-Tate representations
Toby Gee, Mark Kisin
We prove the Breuil-Mézard conjecture for 2-dimensional potentially Barsotti-Tate representations of the absolute Galois group G_K, K a finite extension of Q_p, for any p>2 (up to…
Integral models of Shimura varieties with parahoric level structure, II
Mark Kisin, Georgios Pappas, Rong Zhou
We construct integral models of Shimura varieties of abelian type with parahoric level structure over odd primes. These models are étale locally isomorphic to corresponding local…
Strongly compatible systems associated to semistable abelian varieties
Mark Kisin, Rong Zhou
We prove a motivic refinement of a result of Weil, Deligne and Raynaud on the existence of strongly compatible systems associated to abelian varieties. More precisely, given an abe…
Independence of for Frobenius conjugacy classes attached to abelian varieties
Mark Kisin, Rong Zhou
Let be an abelian variety over a number field and let denote the Mumford--Tate group of . After replacing by a finite ex…