JournalsjncgVol. 1 , No. 3DOI 10.4171/jncg/9

Base change and <var>K</var>-theory for GL(<em>n</em>)

  • Roger Plymen

    University of Manchester, United Kingdom
  • Sergio Mendes

    ISCTE, Lisboa, Portugal
Base change and <var>K</var>-theory for GL(<em>n</em>) cover

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).