Hodge cohomology with a ramification filtration, I

2023/06/12 by Kelly, Shane, Miyazaki, Hiroyasu · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2306.06838

Abstract

We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors ``at infinity''. We show that the filtered pieces have transfers morphisms, fpqc descent, and are so called cube invariant. In the presence of resolution of singularities and weak factorisation they are invariant under blowup ``at infinity''. As such, they lead to a realisation functor from Kahn, Miyazaki, Saito and Yamazaki's category of motives with modulus over a characteristic zero base field.

Cited by

• Solid realization of motives with modulus

Related

• Hodge cohomology with a ramification filtration, II
• Motivic homotopy theory with ramification filtrations
• Filtrations on the Chow groups and transcendence degree
• Filtrations on combinatorial intersection cohomology and invariants of subdivisions
• Blow-up invariance for Hodge-Witt sheaves with modulus