K-theory, chamber homology and base change for the p-ADIC groups SL(2), GL(1) and GL(2)
General Material Designation
[Thesis]
First Statement of Responsibility
Aeal, Wemedh
Subsequent Statement of Responsibility
Rowley, Peter. ; Plymen, Roger.
.PUBLICATION, DISTRIBUTION, ETC
Name of Publisher, Distributor, etc.
University of Manchester
Date of Publication, Distribution, etc.
2012
DISSERTATION (THESIS) NOTE
Dissertation or thesis details and type of degree
Ph.D.
Body granting the degree
University of Manchester
Text preceding or following the note
2012
SUMMARY OR ABSTRACT
Text of Note
The thrust of this thesis is to describe base change BC_E/F at the level of chamber homology and K-theory for some p-adic groups, such as SL(2,F), GL(1,F) and GL(2,F). Here F is a non-archimedean 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. 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 Baum-Connes correspondence for such p-adic groups. This thesis involved the arithmetic of fields such as E and F, geometry of trees, the homology groups and the Weil group W_F.