Number Theory Seminar
Let p be a prime number. The Montreal functor of P. Colmez sends p-adic representations of $\GL_2(\Q_p)$ to p-adic modules for $\Gamma$, where $\Gamma$ denotes the absolute Galois group of $\Q_p$. One result of V. Paskunas' study of the Montreal functor, which was a crucial step toward the p-adic Langlands correspondence for $\GL_2(\Q_p)$, is that its failure to be fully faithful boils down to the fact that it sends the trivial representation to zero. In this talk, for p greater than 3, we introduce a fully faithful alternative to the Montreal functor. It has a different target category: a derived category of modules over the stack of 2-dimensional p-adic representations of $\Gamma$. This is joint work with Christian Johansson and James Newton.