Cyclotomy and analytic geometry over F_1

Details Cyclotomy and analytic geometry over F_1 Cyclotomy and analytic geometry over F_1

2008-09-09

arxiv.org/abs/0809.1564v2

Mathematics

Algebraic Geometry

30 pages

Scientific paper

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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