Langlands correspondence for isocrystals and the existence of crystalline companions for curves

Abstract

In this paper, we show the Langlands correspondence for isocrystals on curves. This shows the existence of crystalline companion in the curve case. For the proof, we construct the theory of arithmetic $\mathcal{D}$-modules for algebraic stacks whose diagonal morphisms are finite.

Cited by in corpus (5)

• A Lefschetz theorem for overconvergent isocrystals with Frobenius structure
• Projective Crystalline Representations of Étale Fundamental Groups and Twisted Periodic Higgs-de Rham Flow
• Rank 2 Local Systems, Barsotti-Tate Groups, and Shimura Curves
• Unipotent monodromy and arithmetic D-modules
• Around the nearby cycle functor for arithmetic $\mathcal{D}$-modules