普适PGL_n字符variety的稳定上同调
代数几何
2026-02-05 v2 代数拓扑
摘要
我们研究的是其fiber over [C]为曲线C上PGL_n-local systems空间的普适PGL_n字符variety。我们利用非阿贝尔Hodge理论和Saito混合Hodge模块的性质，表明从M_g到该variety的Leray-Serre谱序列在E₂阶段即退化。作为应用，我们证明了当g趋于无穷时，这些variety的有理上同调稳定，并计算了稳定极限。我们还推导出针对普适G-character variety的类似结果，该variety位于M_{g,1}上，其fiber over punctuated曲线为G-local systems variety，其中G = GL_n或SL_n。
引用
@article{arxiv.2512.13879,
title = {Stable cohomology of universal character varieties},
author = {Ishan Banerjee and Faye Jackson and Anne Larsen and Sam Payne and Xiyan Zhong},
journal= {arXiv preprint arXiv:2512.13879},
year = {2026}
}
备注
v2: 35 pages; added an appendix by Anne Larsen and Mirko Mauri on the stable intersection cohomology of universal character varieties beyond the smooth case