# Base change and K-theory for GL(n)

Research paper by Sergio Mendes, Roger Plymen

Indexed on: 15 Feb '07Published on: 15 Feb '07Published in: Mathematics - K-Theory and Homology

#### Abstract

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).