Density of potentially crystalline representations of fixed weight

作者：Hellmann Eugen^*; Schraen Benjamin

来源：Compositio Mathematica, 2016, 152(8): 1609-1647.

DOI：10.1112/S0010437X16007363

• p-adic Hodge theory
• (phi, Gamma)-modules
• deformations of Galois representations

Let K be a finite extension of Q(p) and let (rho) over bar be a continuous, absolutely irreducible representation of its absolute Galois group with values in a finite field of characteristic p. We prove that the Galois representations that become crystalline of a fixed regular weight after an abelian extension are Zariski-dense in the generic fiber of the universal deformation ring of (rho) over bar. In fact we deduce this from a similar density result for the space of trianguline representations. This uses an embedding of eigenvarieties for unitary groups into the spaces of trianguline representations as well as the corresponding density claim for eigenvarieties as a global input.

• 出版日期2016-8