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The pro-
$p$-Iwahori Hecke algebra of a reductive 
$p$-adic group I
- Part of
-
- Journal:
- Compositio Mathematica / Volume 152 / Issue 4 / April 2016
- Published online by Cambridge University Press:
- 23 October 2015, pp. 693-753
- Print publication:
- April 2016
-
- Article
-
- You have access
- Export citation
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Let
$R$ be a commutative ring, let 
$F$ be a locally compact non-archimedean field of finite residual field 
$k$ of characteristic 
$p$, and let 
$\mathbf{G}$ be a connected reductive 
$F$-group. We show that the pro-
$p$-Iwahori Hecke 
$R$-algebra of 
$G=\mathbf{G}(F)$ admits a presentation similar to the Iwahori–Matsumoto presentation of the Iwahori Hecke algebra of a Chevalley group, and alcove walk bases satisfying Bernstein relations. This was previously known only for a 
$F$-split group 
$\mathbf{G}$.
