Fun with $\F_1$

Details Fun with $\F_1$ Fun with $\F_1$

2008-06-14

arxiv.org/abs/0806.2401v1

Mathematics

Algebraic Geometry

29 pages, 1 figure

Scientific paper

We show that the algebra and the endomotive of the quantum statistical mechanical system of Bost--Connes naturally arises by extension of scalars from the "field with one element" to rational numbers. The inductive structure of the abelian part of the endomotive corresponds to the tower of finite extensions of that "field", while the endomorphisms reflect the Frobenius correspondences. This gives in particular an explicit model over the integers for this endomotive, which is related to the original Hecke algebra description. We study the reduction at a prime of the endomotive and of the corresponding noncommutative crossed product algebra.

Affiliated with

Also associated with

No associations

Rating

Fun with $\F_1$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fun with $\F_1$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fun with $\F_1$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-258062