Deitmar's versus Toen-Vaquie's schemes over F_1
arXiv:1005.0287 · doi:10.1007/s00209-011-0896-5
Abstract
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.
13 pages. Shorter, final version. To appear in Math. Z. The final publication is available at springerlink.com