The geometry of toric schemes

Abstract

Geometric properties of schemes obtained by gluing algebras of monoids, including separation and finiteness properties, irreducibility, normality, catenarity, dimension, and Serre's properties (S_k) and (R_k), are investigated. This is used to show how the geometry of a toric scheme over an arbitrary base is influenced by the geometry of the base.

to appear in J. Pure Appl. Algebra; corrected typos, updated references

References in corpus (2)

• Mapping F_1-land:An overview of geometries over the field with one element
• Deitmar's versus Toen-Vaquie's schemes over F_1

Cited by in corpus (1)

• The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces