Berthelot's conjecture via homotopy theory

TL;DR

This paper employs motivic and homotopy theoretic methods to provide a concise proof of Berthelot's conjecture, demonstrating that the push-forward of the structural sheaf in rigid cohomology naturally forms an overconvergent F-isocrystal.

Contribution

It introduces a homotopy-theoretic approach to prove Berthelot's conjecture, offering a new perspective and simplifying the proof process.

Findings

Proof of Berthelot's conjecture using motivic methods

Establishment of the canonical overconvergent F-isocrystal structure

Simplification of the proof via homotopy theory

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.