On a theorem of Narasimhan and Ramanan on deformations
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_ | 1866915884727009280 |
|---|---|
| author | Balaji, V. Pandey, Y. |
| author_facet | Balaji, V. Pandey, Y. |
| contents | Let $X$ be a smooth projective curve genus $G$ (as elaborated in \ref{main1}), over an algebraically closed field $k$ of arbitrary characteristics. Let $\cH$ {\em be a tamely ramified absolutely simple, simply connected connected group scheme (see \eqref{quasisplitcase})}. Let $\cM$ denote the moduli stack $\cM_X(\cH)$ of $\cH$-torsors on $X$ and $\cM^{^s}$ be the open substack of {\em stable torsors}. Using the theory of parahoric torsors and Parahoric-correspondences, we describe the cohomology groups $\text{H}^i\left(\cM^{^s}, \cT_{_{\cM}}\right), i = 0,1,2$ and $\text{H}^i\left(\cM^{^s}, Ω_{_{\cM}}\right), i = 0,1,2$ in terms of the curve $X$. The classical results of Narasimhan and Ramanan are derived as a consequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a theorem of Narasimhan and Ramanan on deformations Balaji, V. Pandey, Y. Algebraic Geometry 14D23, 14D20 Let $X$ be a smooth projective curve genus $G$ (as elaborated in \ref{main1}), over an algebraically closed field $k$ of arbitrary characteristics. Let $\cH$ {\em be a tamely ramified absolutely simple, simply connected connected group scheme (see \eqref{quasisplitcase})}. Let $\cM$ denote the moduli stack $\cM_X(\cH)$ of $\cH$-torsors on $X$ and $\cM^{^s}$ be the open substack of {\em stable torsors}. Using the theory of parahoric torsors and Parahoric-correspondences, we describe the cohomology groups $\text{H}^i\left(\cM^{^s}, \cT_{_{\cM}}\right), i = 0,1,2$ and $\text{H}^i\left(\cM^{^s}, Ω_{_{\cM}}\right), i = 0,1,2$ in terms of the curve $X$. The classical results of Narasimhan and Ramanan are derived as a consequence. |
| title | On a theorem of Narasimhan and Ramanan on deformations |
| topic | Algebraic Geometry 14D23, 14D20 |
| url | https://arxiv.org/abs/2506.17574 |