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Title: K-theory, chamber homology and base change for the p-ADIC groups SL(2), GL(1) and GL(2)
Author: Aeal, Wemedh
ISNI:       0000 0004 2721 0200
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2012
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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.
Supervisor: Rowley, Peter. ; Plymen, Roger. Sponsor: Ministry of Higher Education and Scientific Research ; Iraq
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: K-Theory ; Non-Commutative Geometry ; Chamber Homology ; Base Change ; Representation Theory ; Number Theory ; Algebraic Topology