# 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}
}
• Published 2 September 2013
• Mathematics
• Nagoya Mathematical Journal
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…
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