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- W1719932468 abstract "Let $G$ be a connected reductive group over a non-Archimedean local field. We prove that its parahoric subgroups are definable in the Denef-Pas language, which is a first-order language of logic used in the theory of motivic integration developed by Cluckers and Loeser. The main technical result is the definability of the connected component of the N'eron model of a tamely ramified algebraic torus. As a corollary, we prove that the canonical Haar measure on $G$, which assigns volume $1$ to the particular emph{canonical} maximal parahoric defined by Gross, is motivic. This result resolves a technical difficulty that arose in Cluckers-Gordon-Halupczok and Shin-Templier and permits a simplification of some of the proofs in those articles. It also allows us to show that formal degree of a compactly induced representation is a motivic function of the parameters defining the representation." @default.
- W1719932468 created "2016-06-24" @default.
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- W1719932468 date "2015-07-09" @default.
- W1719932468 modified "2023-09-26" @default.
- W1719932468 title "The canonical measure on a reductive p-adic group is motivic" @default.
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- W1719932468 doi "https://doi.org/10.48550/arxiv.1507.02619" @default.
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