λ-环与单元场
Lambda-rings and the field with one element
摘要：
在Grothendieck的Riemann-Roch理论的意义下，λ-环理论是对交换环理论的丰富。同样地，我们可以在整数环Z上丰富通常的代数几何，产生λ-代数几何。我们表明，λ-代数几何是在一个精确的意义上的代数几何在一个更深的基础比Z，它有许多属性预测代数几何在神话领域的一个元素。此外，这是一种既形式上健壮又与算术代数几何中的活跃领域密切相关的方法。
英文摘要：
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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