English

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 pp-adic cohomology theories. In particular, we revisit the proof of the pp-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