## Haar Measure and the Artin Conductor

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- by Benedict H. Gross and Wee Teck Gan PDF
- Trans. Amer. Math. Soc.
**351**(1999), 1691-1704 Request permission

## 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
- MR Author ID: 77400
- Email: gross@math.harvard.edu
**Wee Teck Gan**- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08540
- MR Author ID: 621634
- Email: wtgan@math.princeton.edu
- Received by editor(s): March 4, 1997
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**351**(1999), 1691-1704 - MSC (1991): Primary 11E64
- DOI: https://doi.org/10.1090/S0002-9947-99-02095-4
- MathSciNet review: 1458303