Abstract: In the 90’s Gouvea and Mazur proved that the Galois representations that are (up to twist) associated to modular forms are Zariski-dense in the generic fiber of certain Galois deformation rings. This result was generalized to 3-dimensional polarized Galois representations by Chenevier, using the same strategy involving the so-called ‚infinite fern‘.
I will report on joint work with Christophe Margerin and Benjamin Schraen concerning generalizations of this statement to arbitrary dimensions. This builds upon the analysis of the local geometry of a space of p-adic Galois representations of a prescribed type (so called trianguline representations) and the construction of companion points on eigenvarieties.
Density of automorphic points in polarized Galois deformation spaces
22.01.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: