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SUMMARY:Density of automorphic points in polarized Galois deformation ring
 s - Eugen Hellmann
DTSTART:20180313T143000Z
DTEND:20180313T153000Z
UID:TALK100372@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:In the 90’s Gouvea and Mazur proved that the Galois represen
 tations that are (up to twist) associated to modular forms are \nZariski-d
 ense in the generic fiber of certain Galois deformation rings. This result
  was generalized to 3-dimensional polarized Galois representations by Chen
 evier\, using the same strategy involving the so-called ‚infinite fern
 ‘. \nI will report on joint work with Christophe Margerin and Benjamin S
 chraen concerning generalizations of this statement to arbitrary dimension
 s. This builds upon the analysis of the local geometry of a space of p-adi
 c Galois representations of a prescribed type (so called trianguline repre
 sentations) and the construction of companion points on eigenvarieties. 
LOCATION:MR13
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