Linear and quadratic ranges in representation stability
Linear and quadratic ranges in representation stability
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DOI：
10.1016/j.aim.2018.05.025
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发表时间：
2017-06
影响因子：
1.7
通讯作者：
Thomas Church;Jeremy Miller;Rohit Nagpal;Jens Reinhold
中科院分区：
文献类型：
--
作者：
Thomas Church;Jeremy Miller;Rohit Nagpal;Jens Reinhold
我们证明了关于 FI 模块的频谱序列的两个一般结果。这些结果可用于显着改善目前文献中 FI 模块的大部分稳定性定理的稳定范围。我们详细地解决了配置空间的上同调，其中我们证明了线性稳定范围，以及一般线性群的同余子群的同调，我们证明了二次稳定范围。以前，这些示例中已知的最佳稳定范围是指数范围。在加性常数范围内，我们对同余子群的研究验证了 Djament 的猜想。
We prove two general results concerning spectral sequences ofFI-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems forFI-modules currently in the literature. We work this out in detail for the cohomology of configuration spaces where we prove a linear stable range and the homology of congruence subgroups of general linear groups where we prove a quadratic stable range. Previously, the best stable ranges known in these examples were exponential. Up to an additive constant, our work on congruence subgroups verifies a conjecture of Djament.