2010/05/31 by Alberto Vezzani · 1 citation
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Characterization (materials science) #Coherent sheaf #Commutative property #Equivalence (formal languages) #Equivalence of categories #Functor #Homotopy and Cohomology in Algebraic Topology #Sheaf #math.AG #math.NT
paper · pdf · doi:10.1007/s00209-011-0896-5
13 pages. Shorter, final version. To appear in Math. Z. The final publication is available at springerlink.com
openalex publication_date 2011/05/30 · arxiv created 2011/06/11 · arxiv updated 2011/06/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show the equivalence between Deitmar's and Toen-Vaquie's notions of schemes over F1 (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.