Moduli stacks of Galois representations and the p-adic local Langlands correspondence for GL2(ℚp)

Journal article, 2026

We give a categorical formulation of the p-adic local Langlands correspondence for GL2(ℚp) as an embedding of the derived category of locally admissible representations into the category of Ind-coherent sheaves on the moduli stack of two-dimensional representations of Gal(ℚ̄p/ℚp). The Montréal functor appears as the‘Whittaker coefficient’ for the universal Galois representation, in the sense of the geometric Langlands program. Moreover, we relate our version of the p-adic local Langlands correspondence for GL2(ℚp) to the cohomology of modular curves through a local–global compatibility formula.