Journal of Noncommutative Geometry

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Volume 1, Issue 3, 2007, pp. 311–331
DOI: 10.4171/JNCG/9

Published online: 2007-09-30

Base change and K-theory for GL(n)

Sergio Mendes[1] and Roger Plymen[2]

(1) ISCTE, Lisboa, Portugal
(2) University of 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

Mendes Sergio, Plymen Roger: Base change and K-theory for GL(n). J. Noncommut. Geom. 1 (2007), 311-331. doi: 10.4171/JNCG/9