Shifted Poisson and symplectic structures on derived N-stacks

TL;DR

This paper establishes a canonical equivalence between shifted symplectic and non-degenerate shifted Poisson structures on derived Artin N-stacks, advancing the understanding of their geometric and algebraic relationships.

Contribution

It proves a fundamental equivalence linking shifted symplectic and Poisson structures in derived algebraic geometry, providing new insights into their interplay.

Findings

Canonical equivalence between shifted symplectic and Poisson structures.

Extension of classical structures to derived Artin N-stacks.

Deepens understanding of geometric structures in derived algebraic geometry.

Abstract

We show that on a derived Artin N-stack, there is a canonical equivalence between the spaces of n-shifted symplectic structures and non-degenerate n-shifted Poisson structures.