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Haar measure and the Artin conductor. (English) Zbl 0991.20033

Summary: Let \(G\) be a connected reductive group, defined over a local, non-Archimedean field \(k\). The group \(G(k)\) is locally compact and unimodular. B. H. Gross [Invent. Math. 130, No. 2, 287-313 (1997; Zbl 0904.11014)] defined a Haar measure \(|\omega_G|\) 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.

MSC:

20G25 Linear algebraic groups over local fields and their integers
11G09 Drinfel’d modules; higher-dimensional motives, etc.
43A05 Measures on groups and semigroups, etc.

Citations:

Zbl 0904.11014
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References:

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