Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.
The Riemann-Hilbert Correspondence for Algebraic Stacks
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abstract
Using the theory infinity-categories we construct derived (dg-)categories of regular, holonomic D-modules and algebraically constructible sheaves on a complex smooth algebraic stack. We construct a natural infinity-categorical equivalence between these two categories generalising the classical Riemann-Hilbert correspondence.
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2026 1verdicts
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Positivity in the context of Hodge modules and Higgs bundles on Deligne-Mumford stacks
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.