  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.
