Proves the localization theorem for motivic homotopy theory over complex analytic stacks and supplies general techniques for algebraic and differentiable stacks.
The ´ etale local stru cture of algebraic stacks
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
verdicts
UNVERDICTED 6representative citing papers
Criterion proven for smooth DM stacks to be weighted blow-ups of another stack under bundle and normal bundle conditions, applied to show stable genus one curve moduli is a weighted blow-up of the pseudo-stable stack.
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
Determines local singularity types for Hilbert schemes of ≤7 points in A^3 via an intrinsic Thomason theorem and verifies Zhou's conjecture on tautological sheaf Euler characteristics for ≤6 points on P^3.
Provides spectral description of central torus convolution actions and shows the ℓ-adic categorical Langlands conjecture passes to quotients by central tori in char 0 and for Langlands-Shahidi parameters in all char, extending to PGL_n.
Perverse character varieties are proven to be quasi-affine via a purely stack-theoretic construction exhibiting sections of the structure sheaf.
citing papers explorer
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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.
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A criterion for smooth weighted blow-downs
Criterion proven for smooth DM stacks to be weighted blow-ups of another stack under bundle and normal bundle conditions, applied to show stable genus one curve moduli is a weighted blow-up of the pseudo-stable stack.
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Semiorthogonal decompositions for stacks
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
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On singular Hilbert schemes of points: Local structures and tautological sheaves
Determines local singularity types for Hilbert schemes of ≤7 points in A^3 via an intrinsic Thomason theorem and verifies Zhou's conjecture on tautological sheaf Euler characteristics for ≤6 points on P^3.
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On the action of the center in the $\ell$-adic categorical Langlands program
Provides spectral description of central torus convolution actions and shows the ℓ-adic categorical Langlands conjecture passes to quotients by central tori in char 0 and for Langlands-Shahidi parameters in all char, extending to PGL_n.
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(Quasi-)affineness of perverse character varieties
Perverse character varieties are proven to be quasi-affine via a purely stack-theoretic construction exhibiting sections of the structure sheaf.