A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications
- Ben-Bassat, Oren
- Brav, Chris
- Bussi, V
- Joyce, Dominic
- Bussi, Vittoria
DOIAbstract
This is the fifth in a series arXiv:1304.4508, arXiv:1305,6302, arXiv:1211.3259, arXiv:1305.6428 on the '$k$-shifted symplectic derived algebraic geometry' of Pantev, Toen, Vaquie and Vezzosi, arXiv:1111.3209. This paper extends the previous three from (derived) schemes to (derived) Artin stacks. We prove four main results: (a) If $(X,\omega)$ is a $k$-shifted symplectic derived Artin stack for $k<0$ in the sense of arXiv:1111.3209, then near each $x\in X$ we can find a 'minimal' smooth atlas $\varphi:U\to X$ with $U$ an affine derived scheme, such that $(U,\varphi^*(\omega))$ may be written explicitly in coordinates in a standard 'Darboux form'. (b) If $(X,\omega)$ is a $-1$-shifted symplectic derived Artin stack and $X'$ the underlyin...
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