On Shifted Contact Derived Artin Stacks
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910884693016576 |
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| author | Berktav, Kadri İlker |
| author_facet | Berktav, Kadri İlker |
| contents | This is a sequel of our previous work, arXiv:2209.09686, on the development of derived contact geometry, in which we formally introduced shifted contact structures on derived stacks and proved some results for $k$-shifted contact derived schemes, with $k<0$. In this paper, we extend these results from derived schemes to derived Artin stacks. In brief, we first show that for $k<0$, every $k$-shifted contact derived Artin stack admits a contact Darboux atlas. Secondly, we canonically describe the symplectification of a derived Artin stack equipped with a $k$-shifted contact structure, where $k<0$. Lastly, we give several constructions of contact derived stacks using certain cotangent stacks and shifted prequantization structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03334 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Shifted Contact Derived Artin Stacks Berktav, Kadri İlker Algebraic Geometry This is a sequel of our previous work, arXiv:2209.09686, on the development of derived contact geometry, in which we formally introduced shifted contact structures on derived stacks and proved some results for $k$-shifted contact derived schemes, with $k<0$. In this paper, we extend these results from derived schemes to derived Artin stacks. In brief, we first show that for $k<0$, every $k$-shifted contact derived Artin stack admits a contact Darboux atlas. Secondly, we canonically describe the symplectification of a derived Artin stack equipped with a $k$-shifted contact structure, where $k<0$. Lastly, we give several constructions of contact derived stacks using certain cotangent stacks and shifted prequantization structures. |
| title | On Shifted Contact Derived Artin Stacks |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2401.03334 |