arXiv Open Access 2017

Linear and quadratic ranges in representation stability

Thomas Church Jeremy Miller Rohit Nagpal Jens Reinhold

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Abstrak

We prove two general results concerning spectral sequences of $\mathbf{FI}$-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems for $\mathbf{FI}$-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.

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math.RT math.GN

Penulis (4)

Thomas Church

Jeremy Miller

Rohit Nagpal

Jens Reinhold

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APA MLA BibTeX

Church, T., Miller, J., Nagpal, R., Reinhold, J. (2017). Linear and quadratic ranges in representation stability. https://arxiv.org/abs/1706.03845

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Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓