Wydawnictwa / Czasopisma IMPAN / Acta Arithmetica / Wszystkie zeszyty

Streszczenie

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.