2022/08/22 by Abe, Tomoyuki, Lazda, Christopher
#11G25 #14F30 #14G17 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2208.10137
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^†-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 sp+ for overconvergent isocrystals, which enables us to prove the comparison theorem for compactly supported cohomology.