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Haar Measure and the Artin Conductor


Authors: Benedict H. Gross and Wee Teck Gan
Journal: Trans. Amer. Math. Soc. 351 (1999), 1691-1704
MSC (1991): Primary 11E64
MathSciNet review: 1458303
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Abstract: Let $G$ be a connected reductive group, defined over a local, non-archimedean field $k$. The group $G(k)$ is locally compact and unimodular. In On the motive of a reductive group, Invent. Math. 130 (1997), by B. H. Gross, a Haar measure $|\omega _G|$ was defined on $G(k)$, using the theory of Bruhat and Tits. In this note, we give another construction of the measure $|\omega _G|$, using the Artin conductor of the motive $M$ of $G$ over $k$. The equivalence of the two constructions is deduced from a result of G. Prasad.


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Additional Information

Benedict H. Gross
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: gross@math.harvard.edu

Wee Teck Gan
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08540
Email: wtgan@math.princeton.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02095-4
Received by editor(s): March 4, 1997
Article copyright: © Copyright 1999 American Mathematical Society