Deitmar's versus Toen-Vaquie's schemes over F_1
Algebraic Geometry
2011-06-14 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.1005.0287,
title = {Deitmar's versus Toen-Vaquie's schemes over F_1},
author = {Alberto Vezzani},
journal= {arXiv preprint arXiv:1005.0287},
year = {2011}
}
Comments
13 pages. Shorter, final version. To appear in Math. Z. The final publication is available at springerlink.com