A Jacobian Criterion for Artin $v$-stacks
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914193078222848 |
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| author | Hamann, Linus |
| author_facet | Hamann, Linus |
| contents | We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a smooth quasi-projective variety over the Fargues-Fontaine curve. Namely, we show how to use their criterion to deduce an analogue for spaces of sections of a smooth Artin stack over the (schematic) Fargues-Fontaine curve obtained by taking the stack quotient of a smooth quasi-projective variety by the action of a linear algebraic group. As an application, we show various moduli stacks appearing in the Fargues-Scholze geometric Langlands program are cohomologically smooth Artin $v$-stacks and compute their $\ell$-dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_07495 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Jacobian Criterion for Artin $v$-stacks Hamann, Linus Algebraic Geometry Number Theory Representation Theory We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a smooth quasi-projective variety over the Fargues-Fontaine curve. Namely, we show how to use their criterion to deduce an analogue for spaces of sections of a smooth Artin stack over the (schematic) Fargues-Fontaine curve obtained by taking the stack quotient of a smooth quasi-projective variety by the action of a linear algebraic group. As an application, we show various moduli stacks appearing in the Fargues-Scholze geometric Langlands program are cohomologically smooth Artin $v$-stacks and compute their $\ell$-dimensions. |
| title | A Jacobian Criterion for Artin $v$-stacks |
| topic | Algebraic Geometry Number Theory Representation Theory |
| url | https://arxiv.org/abs/2209.07495 |