We use motivic methods to give a quick proof of Berthelot’s conjecture stating that the pushforward map in rigid cohomology of the structural sheaf along a smooth and proper map has a canonical structure of overconvergent F -isocrystal on the base.
Berthelot’s conjecture via homotopy theory / V. Ertl, A. Vezzani. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - (2025), pp. 1-43. [Epub ahead of print] [10.1215/00127094-2025-0021]
Berthelot’s conjecture via homotopy theory
A. VezzaniUltimo
2025
Abstract
We use motivic methods to give a quick proof of Berthelot’s conjecture stating that the pushforward map in rigid cohomology of the structural sheaf along a smooth and proper map has a canonical structure of overconvergent F -isocrystal on the base.
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