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1 results

  • ORBITAL INTEGRALS FOR LINEAR GROUPS

  • Raf Cluckers, Jan Denef
  • Journal:
    Journal of the Institute of Mathematics of Jussieu / Volume 7 / Issue 2 / April 2008
    Published online by Cambridge University Press:
    10 December 2007, pp. 269-289
    Print publication:
    April 2008

  • For a linear group $G$ acting on an absolutely irreducible variety $X$ over $\mathbb{Q}$, we describe the orbits of $X(\mathbb{Q}_p)$ under $G(\mathbb{Q}_p)$ and of $X(\mathbb{F}_p((t)))$ under $G(\mathbb{F}_p((t)))$ for $p$ big enough. This allows us to show that the degree of a wide class of orbital integrals over $\mathbb{Q}_p$ or $\mathbb{F}_p((t))$ is less than or equal to $0$ for $p$ big enough, and similarly for all finite field extensions of $\mathbb{Q}_p$ and $\mathbb{F}_p((t))$.