# Lambda-rings and the field with one element

@article{Borger2009LambdaringsAT, title={Lambda-rings and the field with one element}, author={James M. Borger}, journal={arXiv: Number Theory}, year={2009} }

The theory of Lambda-rings, in the sense of Grothendieck's Riemann-Roch theory, is an enrichment of the theory of commutative rings. In the same way, we can enrich usual algebraic geometry over the ring Z of integers to produce Lambda-algebraic geometry. We show that Lambda-algebraic geometry is in a precise sense an algebraic geometry over a deeper base than Z and that it has many properties predicted for algebraic geometry over the mythical field with one element. Moreover, it does this is a…

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