19/12/14 10:27:41.78 s6Tab8iq.net
>>397
＞James Borger
URLﾘﾝｸ(ja.wikipedia.org)
一元体 F1
Borger は有限体や整数環からdescentを用いて[8]、F1 を構成している。
[8]
Borger, James (2009), Λ-rings and the field with one element
URLﾘﾝｸ(en.wikipedia.org)
Field with one element F1
Borger used descent to construct it from the finite fields and the integers.[12]
[12]
URLﾘﾝｸ(arxiv.org)
URLﾘﾝｸ(arxiv.org)
Λ-RINGS AND THE FIELD WITH ONE ELEMENT JAMES BORGER 2009
Abstract. The theory of Λ-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 Λ-algebraic geometry. We show that Λ-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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