The field with one element: a quest for a nonexistent object

In the recent years there has been a burst of approaches dealing with the problem of developing a notion of algebraic geometry and theory of motives over a mysterious "field of characteristic one". In this talk we will present some of the original motivations that lead to this search and outline the principal ideas on the main different approaches to the problem, with a particular mention to our own geometrical approach via torified varieties, schemes admitting a stratification by split tori that permits to give an F_1 structure and easily compute the corresponding zeta function.

Javier López Peña