The thrust of this thesis is to describe base change $BC_{E/F}$ at the level of chamber homology and Ktheory for some \lowercase{p}adic groups, such as $SL(2, F)$, $GL(1, F)$ and $GL(2, F)$. Here $F$ is a nonarchimedean local field and $E$ is a Galois extension of $F$. We have had to master the representation theory of $SL(2)$ and $GL(2)$ including the Langlands parameters.\newline\indent The main result is an explicit computation of the effect of base change on the chamber homology groups, each of which is constructed from cycles. This will have an important connection with the BaumConnes correspondence for such padic groups. This thesis involved the arithmetic of fields such as $E$ and $F$, geometry of trees, the homology groups and the Weil group $\mathcal{W}_{F}$.
Date of Award  1 Aug 2012 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Roger Plymen (Supervisor) & Peter Rowley (Supervisor) 

 Representation Theory.
 Algebraic Topology.
 Base Change.
 Number Theory.
 NonCommutative Geometry.
 KTheory.
 Chamber Homology.
$K$theory, chamber homology and base change for the \lowercase{p}adic groups $SL(2)$, $GL(1)$ and $GL(2)$.
Aeal, W. (Author). 1 Aug 2012
Student thesis: Phd