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.
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