Orbital integrals for linear groups

R. Cluckers; J. Denef

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arXiv · math/0703704

Orbital integrals for linear groups

R. Cluckers·J. Denef

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Abstract

For a linear group $G$ acting on an absolutely irreducible variety $X$ over the rationals $\QQ$, we describe the orbits of $X(\QQ_p)$ under $G(\QQ_p)$ and of $X(\FF_p((t)))$ under $G(\FF_p((t)))$ for $p$ big enough. This allows us to show that the degree of a wide class of orbital integrals over $\QQ_p$ or $\FF_p((t))$ is $\leq 0$ for $p$ big enough, and similarly for all finite field extensions of $\QQ_p$ and $\FF_p((t))$.

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BibTeX RIS

R. Cluckers, J. Denef. 2007-03-23. Orbital integrals for linear groups. https://arxiv.org/abs/math/0703704

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