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

Volume 186 / 2018

Karol Kozioł Acta Arithmetica 186 (2018), 349-376 MSC: Primary 20C08, 20J06; Secondary 16E30. DOI: 10.4064/aa170903-24-3 Published online: 9 November 2018


Let $p\ge 5$ 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 ${\rm H}^1(I_1,C)$ and ${\rm H}^{{\rm top}}(I_1,C)$ when the root system of $G$ is irreducible. We also give some partial results in the general case.


  • Karol KoziołDepartment of Mathematics
    University of Toronto
    40 St. George Street
    Toronto, ON M5S 2E4, Canada

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