Berthelot's conjecture via homotopy theory
arXiv:2406.02182
Abstract
We use motivic methods to give a quick proof of Berthelot's conjecture stating that the push-forward 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.
34 pages. The comparison to Berthelot's rigid cohomology has been expanded. To appear in Duke