A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

Abstract

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.

Authors

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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image