We survey over some recent applications of motivic homotopy theory in the definition and the study of p-adic cohomology theories. In particular, we revisit the proof of the p-adic weight-monodromy conjecture for smooth projective hypersurfaces in light of the motivic definition of nearby cycles and monodromy operators.
A motivic approach to rational p-adic cohomologies / F. Binda, A.V. (CONTEMPORARY MATHEMATICS). - In: Regulators V[s.l] : American Mathematical Society, 2026. - ISBN 9781470485870. - pp. 45-75 (( 5. Conference : 3 - 13 June Evanston 2024.
A motivic approach to rational p-adic cohomologies
F. Binda;A. Vezzani
2026
Abstract
We survey over some recent applications of motivic homotopy theory in the definition and the study of p-adic cohomology theories. In particular, we revisit the proof of the p-adic weight-monodromy conjecture for smooth projective hypersurfaces in light of the motivic definition of nearby cycles and monodromy operators.
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