TL;DR
This paper develops a new formalism for motivic Hodge modules that extends and enhances existing frameworks, providing a categorical structure with compatible realization functors for schemes over complex numbers.
Contribution
It introduces a quasi-categorically enhanced six-functor formalism for motivic Hodge modules with canonical realization functors, advancing the theoretical foundation.
Findings
Constructed a new six-functor formalism for motivic Hodge modules.
Ensured compatibility with Grothendieck's six functors on constructible objects.
Provided a categorical enhancement aligning with M. Saito's derived categories.
Abstract
We construct a quasi-categorically enhanced Grothendieck six-functor formalism on schemes of finite type over the complex numbers. In addition to satisfying many of the same properties as M. Saito's derived categories of mixed Hodge modules, this new six-functor formalism receives canonical motivic realization functors compatible with Grothendieck's six functors on constructible objects.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology