Proves the localization theorem for motivic homotopy theory over complex analytic stacks and supplies general techniques for algebraic and differentiable stacks.
Motivic Hodge modules
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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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2026 1verdicts
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The Localization Theorem for the Motivic Homotopy Theory of Complex Analytic Stacks and other Geometric Settings
Proves the localization theorem for motivic homotopy theory over complex analytic stacks and supplies general techniques for algebraic and differentiable stacks.