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Journal of Noncommutative Geometry

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Base change and K-theory for GL(n)

Sergio Mendes (1) and Roger Plymen (2)

(1) ISCTE, Av. das Forças Armadas, 1649-026, LISBOA, PORTUGAL
(2) School of Mathematics, University of Manchester, Oxford Road, M13 9PL, MANCHESTER, UNITED KINGDOM

Let F be a nonarchimedean local field and let G = GL(n) = GL(n, F). Let E/F be a finite Galois extension. We investigate base change E/F at two levels: at the level of algebraic varieties, and at the level of K-theory. We put special emphasis on the representations with Iwahori fixed vectors, and the tempered spectrum of GL(1) and GL(2). In this context, the prominent arithmetic invariant is the residue degree f(E/F).

Keywords: Local field, general linear group, algebraic variety, base change, K-theory