Hecke module structure on first and top pro-p-Iwahori cohomology

Kozioł, Karol

doi:10.4064/aa170903-24-3

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Hecke module structure on first and top pro-p-Iwahori cohomology

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Kozioł, Karol
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4064/aa170903-24-3
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arXiv:1708.03013.pdf
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Citation

Kozioł, K. (2018). Hecke module structure on first and top pro-p-Iwahori cohomology. Acta Arithmetica, 186(4), 349-376. doi:10.4064/aa170903-24-3.

Cite as: https://hdl.handle.net/21.11116/0000-0003-D15A-C

Abstract

Let $p\geq 5$ be a prime number, $G$ a split connected reductive group defined over a $p$-adic field, and $I_1$ a choice of pro-$p$-Iwahori subgroup. Let $C$ be an algebraically closed field of characteristic $p$ and $\mathcal{H}$ the pro-$p$-Iwahori-Hecke algebra over $C$ associated to $I_1$. We compute the action of $\mathcal{H}$ on $\textrm{H}^1(I_1,C)$
and $\textrm{H}^{\textrm{top}}(I_1,C)$ when the root system of $G$ is
irreducible. We also give some partial results in the general case.