Kavli Affiliate: Tomoyuki Abe
| Summary:
The goal of this article is to prove a comparison theorem between rigid cohomology and cohomology computed using the theory of arithmetic $mathscrD$-modules. To do this, we construct a specialisation functor from Le Stum’s category of constructible isocrystals to the derived category of arithmetic $mathscrD$-modules. For objects `of Frobenius type’, we show that the essential image of this functor consists of overholonomic $mathscrD^dagger$-modules, and lies inside the heart of the dual constructible t-structure. We use this to give a more global construction of Caro’s specialisation functor $mathrmsp_+$ for overconvergent isocrystals, which enables us to prove the comparison theorem for compactly supported cohomology.
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