| Title:
|
On shifted contact derived Artin stacks (English) |
| Author:
|
Berktav, Kadri İlker |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
9 |
| Issue:
|
2 |
| Year:
|
2025 |
| Pages:
|
103-135 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This is a sequel of [2] on the development of derived contact geometry. In [2], we formally introduced shifted contact structures on derived stacks. We then gave a Darboux-type theorem and the notion of symplectification only for negatively shifted contact derived schemes. In this paper, we extend the results of [2] from derived schemes to derived Artin stacks and provide some examples of contact 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. (English) |
| Keyword:
|
derived algebraic geometry |
| Keyword:
|
shifted symplectic structures |
| Keyword:
|
contact geometry |
| MSC:
|
14A20 |
| MSC:
|
14A30 |
| MSC:
|
14F08 |
| idMR:
|
MR4994252 |
| DOI:
|
10.21136/HS.2025.12 |
| . |
| Date available:
|
2026-03-13T14:51:04Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153494 |
| . |
| Reference:
|
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| Reference:
|
[2] Berktav, K.İ.: Shifted contact structures and their local theory..Annales de la Faculté des sciences de Toulouse: Mathématiques, 33(4):1019-1057, 2024. Arxiv:2209.09686 http://arxiv.org/pdf/2209.09686 MR 4862512 |
| Reference:
|
[3] Brav, C., Bussi, V., Joyce, D.: A ‘Darboux’ theorem for derived schemes with shifted symplectic structure..Journal of the American Mathematical Society, 32(2):399-443, 2019. Arxiv:1305.6302 http://arxiv.org/pdf/1305.6302 MR 3904157 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
