Deformation theory of Galois representations

• Applicant: Professor Dr. Vytautas Paskunas
• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 517234220

Deformation theory of Galois representations plays an important role in the Langlands correspondence. During the first funding period we have defined a moduli space of continuous representations of a profinite group, which satisfies Mazur's finiteness condition at p, valued in a generalised reductive group. Thereby we generalised a construction of Wang-Erickson for the general linear group. We have studied the geometry of this moduli space, when the profinite group is an absolute Galois group of a p-adic field and used it to establish ring theoretic properties of local deformation rings. In the follow up project we would like to use these results to investigate the closure of loci, defined by conditions coming from p-adic Hodge theory, in local deformation spaces, study the geometry of the morphisms induced by functoriality between moduli spaces of local Galois representations and also understand the singularities of these moduli spaces and their special fibres. Moreover, we would like to study the geometry of these moduli spaces in the number field case by employing Galois theoretic and automorphic methods.

• DFG Programme: Research Grants