Shifted symplectic structures

Short summary

This paper introduces n-shifted symplectic structures, a generalization of symplectic structures, and proves their existence on classifying stacks of reductive groups and derived stacks of perfect complexes. It establishes a main theorem showing that for a derived Artin stack F with an n-symplectic structure, the derived mapping stack Map(X, F) carries an (n-d)-symplectic structure when X satisfies a Calabi-Yau condition in dimension d.

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