Liquid Tannaka Duality I: Classical Case
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915647802310656 |
|---|---|
| author | Qaisar, Waleed Taroyan, Gregory |
| author_facet | Qaisar, Waleed Taroyan, Gregory |
| contents | We prove a Tannaka duality statement for geometric stacks in the setting of analytic stacks modelled on globally finitely presented Stein spaces. The key ingredient is the theory of liquid vector spaces and liquid quasicoherent sheaves of Clausen-Scholze. As an application, we reconstruct the topological fundamental group of any complex algebraic variety from its category of liquid local systems. We also reconstruct a series of "twisted fundamental groupoids" whose representations correspond to meromorphic flat connections on the complex affine line with logarithmic or irregular singularities at the origin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Liquid Tannaka Duality I: Classical Case Qaisar, Waleed Taroyan, Gregory Algebraic Geometry Complex Variables Differential Geometry We prove a Tannaka duality statement for geometric stacks in the setting of analytic stacks modelled on globally finitely presented Stein spaces. The key ingredient is the theory of liquid vector spaces and liquid quasicoherent sheaves of Clausen-Scholze. As an application, we reconstruct the topological fundamental group of any complex algebraic variety from its category of liquid local systems. We also reconstruct a series of "twisted fundamental groupoids" whose representations correspond to meromorphic flat connections on the complex affine line with logarithmic or irregular singularities at the origin. |
| title | Liquid Tannaka Duality I: Classical Case |
| topic | Algebraic Geometry Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2511.23180 |