• Corpus ID: 115176626

# Characteristic one, entropy and the absolute point

@article{Connes2009CharacteristicOE,
title={Characteristic one, entropy and the absolute point},
author={Alain Connes and Caterina Consani},
journal={arXiv: Algebraic Geometry},
year={2009}
}
• Published 18 November 2009
• Mathematics
• arXiv: Algebraic Geometry
We show that the mathematical meaning of working in characteristic one is directly connected to the fields of idempotent analysis and tropical algebraic geometry and we relate this idea to the notion of the absolute point. After introducing the notion of "perfect" semi-ring of characteristic one, we explain how to adapt the construction of the Witt ring in positive characteristic to the limit case of characteristic one. This construction unveils an interesting connection with entropy and…

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