A motivic approach to rational p-adic cohomologies

2025/08/22 by Binda, Federico, Vezzani, Alberto
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.16196

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.

Citations

• A motivic proof of the finiteness of relative de Rham cohomology
• Berthelot's conjecture via homotopy theory
• Log motivic nearby cycles
• Weil cohomology theories and their motivic Hopf algebroids
• Motivic monodromy and p-adic cohomology theories
• On the p-adic weight-monodromy conjecture for complete intersections in toric varieties
• Pseudocoherent and Perfect Complexes and Vector Bundles on Analytic Adic Spaces
• Triangulated categories of logarithmic motives over a field
• Rigid analytic reconstruction of Hyodo--Kato theory
• On p-adic comparison theorems for rigid analytic varieties, I
• K-theory of valuation rings
• Weil-étale cohomology and Zeta-values of proper regular arithmetic schemes
• Nilpotence and descent in equivariant stable homotopy theory
• Foundations of Rigid Geometry I
• Perfectoid spaces
• Relative log convergent cohomology and relative rigid cohomology I

Related

• Motivic monodromy and p-adic cohomology theories
• Syntomic cohomology and p-adic motivic cohomology
• A motivic integral p-adic cohomology
• Motivic p-adic tame cohomology
• On the p-adic weight-monodromy conjecture for complete intersections in toric varieties