Kavli Affiliate: Tomoyuki Abe
| First 5 Authors: Tomoyuki Abe, Christopher Lazda, , ,
| Summary:
The goal of this article is to prove a comparison theorem between rigid
cohomology and cohomology computed using the theory of arithmetic
$mathscr{D}$-modules. To do this, we construct a specialisation functor from
Le Stum’s category of constructible isocrystals to the derived category of
arithmetic $mathscr{D}$-modules. For objects `of Frobenius type’, we show that
the essential image of this functor consists of overholonomic
$mathscr{D}^dagger$-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 $mathrm{sp}_+$ for overconvergent isocrystals,
which enables us to prove the comparison theorem for compactly supported
cohomology.
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