Projective spaces over    F   1  ℓ | Zendy

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Projective spaces over F 1 ℓ

Author(s) -

Thas Koen

Publication year - 2019

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.21639

Subject(s) - mathematics , morphism , projective space , projective test , space (punctuation) , set (abstract data type) , field (mathematics) , pure mathematics , combinatorics , discrete mathematics , computer science , programming language , operating system

In this essay, we study various notions of projective space (and other schemes) over F 1 ℓ , with F 1 denoting the field with one element. Our leading motivation is the “Hidden Points Principle,” which shows a huge deviation between the set of rational points as closed points defined over F 1 ℓand the set of rational points defined as morphisms ( F 1 ℓ ) ↦ X . We also introduce, in the same vein as Kurokawa [Proc. Jpn. Acad. Ser. A Math. Sci. 81 (2005), pp. 180–184], schemes of F 1 ℓ ‐type and consider their zeta functions.

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