On the notion of geometry over F₁


Katia Consani (The Johns Hopkins University)

Abstract:

In the first part of the talk I will give an overview of the notion of geometry over the ``field with one element" as originally developed by J. Tits and lately re-considered from an algebro-geometric/number-theoretic viewpoint by several authors such as Y. Manin and C. Soule. In the second part of the talk I will explain how and why Chevalley schemes are examples of varieties defined over a quadratic extension of F_1, by introducing a new formulation of the notion of an algebraic variety over such "field". (A joint work with A. Connes)