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 F\(_1\)" 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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