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.
Good Moduli Spaces in Derived Algebraic Geometry
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abstract
We develop a theory of good moduli spaces for derived Artin stacks, which naturally generalizes the classical theory of good moduli spaces introduced by Alper. As such, many of the fundamental results and properties regarding good moduli spaces for classical Artin stacks carry over to the derived context. In fact, under natural assumptions, often satisfied in practice, we show that the derived theory essentially reduces to the classical theory. As applications, we establish derived versions of the \'{e}tale slice theorem for good moduli spaces and the partial desingularization procedure of good moduli spaces.
fields
math.AG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Perverse character varieties are proven to be quasi-affine via a purely stack-theoretic construction exhibiting sections of the structure sheaf.
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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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(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.