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arxiv: 1612.08101 · v2 · pith:IZ7RVAKGnew · submitted 2016-12-23 · 🧮 math.AG · math.AT· math.SG

Shifted cotangent stacks are shifted symplectic

classification 🧮 math.AG math.ATmath.SG
keywords shiftedstackscanonicalcarrycotangentprovestructuresymplectic
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We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true but no written proof was available in the Artin case.

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    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.