• Corpus ID: 15334117

Cyclotomy and analytic geometry over F_1

@article{Manin2008CyclotomyAA,
  title={Cyclotomy and analytic geometry over F\_1},
  author={Yuri I. Manin},
  journal={arXiv: Algebraic Geometry},
  year={2008}
}
  • Y. Manin
  • Published 9 September 2008
  • Mathematics
  • arXiv: Algebraic Geometry
Geometry over non--existent "field with one element" $F_1$ conceived by Jacques Tits [Ti] half a century ago recently found an incarnation, in at least two related but different guises. In this paper I analyze the crucial role of roots of unity in this geometry and propose a version of the notion of "analytic functions" over $F_1$. The paper combines a focused survey with some new constructions. In new version, several local additions and changes are made, references added. 
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