Density of automorphic points in polarized Galois deformation rings

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• Eugen Hellmann
• Tuesday 13 March 2018, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jack Thorne.

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.

This talk is part of the Number Theory Seminar series.

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