Modulo p representations of p-adic reductive groups

• Applicant: Professor Dr. Vytautas Paskunas
• Subject Area: Mathematics
• Term: from 2007 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 42553787

• Final Report Year: 2009

Final Report Abstract

We have studied representations of GL2(F) on Fp-vector spaces, F/Qp finite. When F = Qp the theory is well understood, and we have settled some of the remaining open questions. When F ≠ Qp very little was known before the start of the project, and now we may say that the situation is much more complicated than originally expected. This of course motivates further research. The main question is do all the representations that we have constructed have an arithmetical meaning? If not, how can one single out the "arithmetic" ones?

Publications

• Admissible unitary completions of locally Qp-rational representations of GL2(F)
  Vytautas Paskunas
  
• Extensions for supersingular representations of GL2(Qp), Astérisque
  Vytautas Paskunas
  
• On some crystalline representations of GL2(Qp), Algebra and Number Theory
  Vytautas Paskunas
  
• On the effaceability of certain δ-functors
  Vytautas Paskunas
  
• Towards a modulo p Langlands correspondence for GL2
  Vytautas Paskunas, C. Breuil