Date of Award
2012
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
McDonald, Patrick
Keywords
Bost-Connes Systems, Explicit Class Field Theory, C* Dynamical System
Area of Concentration
Mathematics
Abstract
Following the 1995 paper of Bost and Connes, which defined the Bost-Connes system C_Q, we define and study a C*-dynamical system C_Qp related to the class field theory of Qp. We consider quotients of a pair (?,?_0) of discrete two-by-two matrix groups and show that there is a map from the corresponding Hecke algebra A(?, ?_0) to the algebra of unitary operators on \ell^2(?/?_0). Extending this map to the closure of A(?,?_0) in a regular representation of \ell^2(?/?_0) gives C_Qp. A presentation in terms of two classes of generators is given, and is used to find a representation of A(?,?_0), which is conjectured to extend to a covariant representation of C_Qp having partition function equal to the Euler factor of the Riemann zeta function at p.
Recommended Citation
Gunton, Cody, "A BOST-CONNES SYSTEM FOR Qp" (2012). Theses & ETDs. 4601.
https://digitalcommons.ncf.edu/theses_etds/4601