Deitmar's versus Toen-Vaquie's schemes over F_1

Details Deitmar's versus Toen-Vaquie's schemes over F_1 Deitmar's versus Toen-Vaquie's schemes over F_1

2010-05-03

arxiv.org/abs/1005.0287v2

Mathematics

Algebraic Geometry

13 pages. Shorter, final version. To appear in Math. Z. The final publication is available at springerlink.com

Scientific paper

10.1007/s00209-011-0896-5

We show the equivalence between Deitmar's and Toen-Vaquie's notions of
schemes over F_1 (the 'field with one element'), establishing a symmetry with
the classical case of schemes, seen either as spaces with a structure sheaf, or
functors of points. In proving so, we also conclude some new basic results on
commutative algebra of monoids.

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