• Corpus ID: 7040380

Lambda-rings and the field with one element

  title={Lambda-rings and the field with one element},
  author={James M. Borger},
  journal={arXiv: Number Theory},
  • J. Borger
  • Published 17 June 2009
  • Mathematics, Computer Science
  • arXiv: Number Theory
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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