Lambda-rings and the field with one element

By James M. Borger. 2009

69 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7126972a549220ee5748cd1e39a1cc3af065cb90

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In Algebra and Number Theory

1. L. Hesselholt
2. Thomas H. Geisser

In Geometry and Topology

1. L. Hesselholt
2. A. Mathew
3. Dustin Clausen
4. M. Morrow
5. Thomas H. Geisser

In Mathematical Physics

1. L. Hesselholt
2. A. Mathew
3. Dustin Clausen
4. M. Morrow
5. Thomas H. Geisser

Citations in the corpus

• The big de Rham–Witt complex (2010, methodology): “The reader is also referred to the very readable account by Bergman [14, Appendix] and tothe more modern and general exposition by Borger [2].”