Homology Bases Arising from Reductive Groups Over a Finite Field

Abstract

Let G be a connected reductive algebraic group over k, an algebraic closure of a finite field F q with q elements. Assume that we are given an F q -rational structure on G with Frobenius map F: G → G. Let \(\bar{\mathbb{Q}}{{}_{l}}\) be an algebraic closure of the l-adic numbers (l is a fixed prime number, invertible in F q ).