Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.775315 |
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Title: | Bost-Connes type dynamics and arithmetic of function fields | ||||||
Author: | Bassett, Matthew E. |
ISNI:
0000 0004 7962 4915
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Awarding Body: | Queen Mary, University of London | ||||||
Current Institution: | Queen Mary, University of London | ||||||
Date of Award: | 2019 | ||||||
Availability of Full Text: |
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Abstract: | |||||||
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.
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Supervisor: | Not available | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.775315 | DOI: | Not available | ||||
Keywords: | Mathematical Sciences ; Bost-Connes system ; Function Field Arithmetic | ||||||
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