# Projective geometry in characteristic one and the epicyclic category

@article{Connes2015ProjectiveGI, title={Projective geometry in characteristic one and the epicyclic category}, author={Alain Connes and Caterina Consani}, journal={Nagoya Mathematical Journal}, year={2015}, volume={217}, pages={95 - 132} }

Abstract We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield of max-plus integers ℤmax. Finite-dimensional vector spaces are replaced by modules defined by restriction of scalars from the one-dimensional free module, using the Frobenius endomorphisms of ℤmax. The associated projective spaces are finite and provide a…

## 12 Citations

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Cyclic Theories

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We describe a geometric theory classified by Connes-Consani’s epicylic topos and two related theories respectively classified by the cyclic topos and by the topos [ℕ∗,Set]$[{\mathbb N}^{\ast },…

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We classify the semifields and division semirings containing the max-plus semifield Zmax, which are finitely generated as Zmax-semimodules.

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