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).
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Roger Plymen, Sergio Mendes, Base change and <var>K</var>-theory for GL(<em>n</em>). J. Noncommut. Geom. 1 (2007), no. 3, pp. 311–331DOI 10.4171/JNCG/9