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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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