Schemes over F 1
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چکیده
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 ...
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1 Affine Morphisms Definition 1. Let f : X −→ Y be a morphism of schemes. Then we say f is an affine morphism or that X is affine over Y , if there is a nonempty open cover {Vα}α∈Λ of Y by open affine subsets Vα such that for every α, fVα is also affine. If X is empty (in particular if Y is empty) then f is affine. Any morphism of affine schemes is affine. Any isomorphism is affine, and the aff...
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متن کامل2 1 A pr 2 00 4 Schemes over F 1 Anton
The approach of Kurokawa, Ochiai, and Wakayama to ‘absolute mathematics’ is used to develop a theory of schemes over F1. It turns out that the functor GLn is represented by a scheme and that its value on F1 gives the Weyl group.
متن کامل2 3 A pr 2 00 4 Schemes over F 1 Anton Deitmar
The approach of Kurokawa, Ochiai, and Wakayama to ‘absolute mathematics’ is used to develop a theory of schemes over F1. It turns out that the functor GLn is represented by a scheme and that its value on F1 gives the Weyl group.
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تاریخ انتشار 2004