Shifted cotangent stacks are shifted symplectic
Damien Calaque
TL;DR
The paper proves that shifted cotangent stacks inherently possess a canonical shifted symplectic structure, and shifted conormal stacks have a canonical Lagrangian structure, confirming longstanding beliefs with formal proofs.
Contribution
It provides the first written proof that shifted cotangent stacks are shifted symplectic and shifted conormal stacks are Lagrangian, especially in the Artin case.
Findings
Shifted cotangent stacks carry a canonical shifted symplectic structure.
Shifted conormal stacks carry a canonical Lagrangian structure.
Results confirm longstanding beliefs in derived algebraic geometry.
Abstract
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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