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math.AG 3

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Semiorthogonal decompositions for stacks

math.AG · 2026-05-25 · unverdicted · novelty 6.0

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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  • Hecke operators on symplectic surfaces and $\chi$-independence math.AG · 2026-07-01 · unverdicted · none · ref 35

    Proves Toda's chi-independence conjecture and identifies BPS Lie algebra with tautological classes for one-dimensional Mukai vectors using Hecke operators and bialgebra structures.

  • Semiorthogonal decompositions for stacks math.AG · 2026-05-25 · unverdicted · none · ref 47

    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.

  • (Quasi-)affineness of perverse character varieties math.AG · 2026-05-24 · unverdicted · none · ref 24

    Perverse character varieties are proven to be quasi-affine via a purely stack-theoretic construction exhibiting sections of the structure sheaf.