Stable cohomology of universal character varieties
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912874293624832 |
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| author | Banerjee, Ishan Jackson, Faye Larsen, Anne Payne, Sam Zhong, Xiyan |
| author_facet | Banerjee, Ishan Jackson, Faye Larsen, Anne Payne, Sam Zhong, Xiyan |
| contents | We study the universal PGL_n$character variety over M_g whose fiber over a point [C] is the space of PGL_n-local systems on the curve C. We use nonabelian Hodge theory and properties of Saito's mixed Hodge modules to show that the Leray-Serre spectral sequence for the projection to M_g degenerates at E_2. As an application, we prove that the rational cohomology of these varieties stabilizes as g goes to infinity and compute the stable limit. We also deduce similar results for the universal G-character variety over M_{g,1} whose fiber over a punctured curve is the variety of G-local systems with fixed central monodromy around the puncture, for G = GL_n or SL_n. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable cohomology of universal character varieties Banerjee, Ishan Jackson, Faye Larsen, Anne Payne, Sam Zhong, Xiyan Algebraic Geometry Algebraic Topology 14D20, 14D22, 14H10, 57K20 We study the universal PGL_n$character variety over M_g whose fiber over a point [C] is the space of PGL_n-local systems on the curve C. We use nonabelian Hodge theory and properties of Saito's mixed Hodge modules to show that the Leray-Serre spectral sequence for the projection to M_g degenerates at E_2. As an application, we prove that the rational cohomology of these varieties stabilizes as g goes to infinity and compute the stable limit. We also deduce similar results for the universal G-character variety over M_{g,1} whose fiber over a punctured curve is the variety of G-local systems with fixed central monodromy around the puncture, for G = GL_n or SL_n. |
| title | Stable cohomology of universal character varieties |
| topic | Algebraic Geometry Algebraic Topology 14D20, 14D22, 14H10, 57K20 |
| url | https://arxiv.org/abs/2512.13879 |