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

By Tomoyuki Abe. 2013

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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 $\mathscr{D}$-modules for algebraic stacks whose diagonal morphisms are finite.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cf8fd0bf5e2501c61b249bf1178e08f05d8ecc5b