A motivic approach to rational $p$-adic cohomologies
Algebraic Geometry
2025-08-25 v1
Abstract
We survey over some recent applications of motivic homotopy theory in the definition and the study of -adic cohomology theories. In particular, we revisit the proof of the -adic weight-monodromy conjecture for smooth projective hypersurfaces in light of the motivic definition of nearby cycles and monodromy operators.
Keywords
Cite
@article{arxiv.2508.16196,
title = {A motivic approach to rational $p$-adic cohomologies},
author = {Federico Binda and Alberto Vezzani},
journal= {arXiv preprint arXiv:2508.16196},
year = {2025}
}
Comments
28 pages, prepared for the "Regulators V" conference, Pisa, June 3-13, 2024