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A motivic approach to rational $p$-adic cohomologies
Published 22 Aug 2025 in math.AG | (2508.16196v1)
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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