Langworthy, Andrew (2015). Chevalley group schemes as varieties over the field of one element. University of Birmingham. M.Res.
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Langworthy14PhD.pdf
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Abstract
The “field of one element" is a concept first suggested by J. Tits in 1957. It has been worked on and redefined many times over the past fifty years; in this paper we consider varieties over a quadratic extension of this field, introduced by C. Soule and then refined by Connes and Consani. We follow the Connes and Consani paper “On The Notion Of Geometry Over F1" and present their results along with the necessary introduction to Chevalley groups and algebraic geometry.
| Type of Work: | Thesis (Masters by Research > M.Res.) | |||||||||
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| Award Type: | Masters by Research > M.Res. | |||||||||
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| College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | |||||||||
| School or Department: | School of Mathematics | |||||||||
| Funders: | None/not applicable | |||||||||
| Subjects: | Q Science > QA Mathematics | |||||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/5464 |
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