### Lambda-rings and the field with one element

**Abstract:**

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 way that is both formally robust and closely related to active areas in
arithmetic algebraic geometry.

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The paper's page at arxiv.org

#### Release notes

2009-Jun-17: Archive release