Geometry of monoids and F_1- schemes.

by Dr Rekha Santhanam (Indian Institute of Technology, Kanpur.)

Monday 14 Feb 2011, 16:00 → 17:30 Asia/Kolkata

AG-77 (Colaba Campus)

Lately there has been a lot of interest in the field of one element denoted by F_1 in the context of arithmetic geometry and number theory. The definition of such a field is guided by what happens to the geometry over F_1 as q tends to 1. In this talk we will define F_1-schemes as defined by Connes and Consani. We will define algebraic K-theory of F_1-schemes and in particular show that the K-theory of F_1 is the stable homotopy groups of spheres. This is a joint work with Chenghao Chu and Oliver Lorschied.