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arXiv · 2607.00088

Central isogenies and conjugacy classes in reductive groups

Sean Cotner
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Abstract

Steinberg described the group of components of the centralizer of a semisimple element of a connected semisimple algebraic group $G$ as a subgroup of the fundamental group of $G$. We show that this description can be generalized to explain the fact that centralizers of unipotent elements can fail to be reduced when the universal cover of $G$ is not étale. As applications, we compute generic multiplicities in the special fibers of moduli spaces of L-parameters and universal deformation rings, and we show there is no Springer isomorphism for $\mathrm{PGL}_p$ in characteristic $p$.

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Sean Cotner. 2026-06-30. Central isogenies and conjugacy classes in reductive groups. https://arxiv.org/abs/2607.00088

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