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Title: Bost-Connes type dynamics and arithmetic of function fields
Author: Bassett, Matthew E.
ISNI:       0000 0004 7962 4915
Awarding Body: Queen Mary, University of London
Current Institution: Queen Mary, University of London
Date of Award: 2019
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The work of this thesis falls within two main themes: the analogy between number fields and function fi elds of an algebraic curve over a fi nite fi eld; and the recovery of arithmetic information from the Bost-Connes system associated to such global fields. We present a new construction for Bost-Connes systems for function fi elds based on the ring of S-integers and show that it provides a suitable framework to generalize the work of Takeishi to the functionfi eld case and thus recover class numbers. Further, we investigate an analogue of the Deligne-Ribet topological dynamical system that appears in Bost-Connes systems and show that isomorphisms that respect these dynamics are equivalent to arithmetic equivalences of the related global fields.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematical Sciences ; Bost-Connes system ; Function Field Arithmetic