2 2 M ay 2 00 6 Remarks on zeta functions and K - theory over F 1
نویسنده
چکیده
We show that the notion of zeta functions over the field of one element F1, as given in special cases by Soulé, extends naturally to all F1-schemes as defined by the author in an earlier paper. We further give two constructions of K-theory for affine schemes or F1-rings, we show that these coincide in the group case, but not in general.
منابع مشابه
ar X iv : 0 90 3 . 20 24 v 3 [ m at h . A G ] 9 J ul 2 00 9 SCHEMES OVER F 1 AND ZETA FUNCTIONS
We determine the real counting function N (q) (q ∈ [1, ∞)) for the hypothetical " curve " C = Spec Z over F 1 , whose corresponding zeta function is the complete Riemann zeta function. Then, we develop a theory of functorial F 1-schemes which reconciles the previous attempts by C. Soulé and A. Deitmar. Our construction fits with the geometry of monoids of K. Kato, is no longer limited to toric ...
متن کاملar X iv : 0 90 3 . 20 24 v 3 [ m at h . A G ] 9 J ul 2 00 9 SCHEMES OVER F 1 AND ZETA FUNCTIONS
We determine the real counting function N (q) (q ∈ [1, ∞)) for the hypothetical " curve " C = Spec Z over F 1 , whose corresponding zeta function is the complete Riemann zeta function. Then, we develop a theory of functorial F 1-schemes which reconciles the previous attempts by C. Soulé and A. Deitmar. Our construction fits with the geometry of monoids of K. Kato, is no longer limited to toric ...
متن کامل