Ample families, multihomogeneous spectra, and algebraization of formal schemes
Algebraic Geometry
2007-05-23 v3
Abstract
Generalizing homogeneous spectra for rings graded by natural numbers, we introduce multihomogeneous spectra for rings graded by abelian groups. Such homogeneous spectra have the same completeness properties as their classical counterparts, but are possibly nonseparated. We relate them to ample families of invertible sheaves and simplicial toric varieties. As an application, we generalize Grothendieck's Algebraization Theorem and show that formal schemes with certain ample families are algebraizable.
Keywords
Cite
@article{arxiv.math/0012082,
title = {Ample families, multihomogeneous spectra, and algebraization of formal schemes},
author = {Holger Brenner and Stefan Schroeer},
journal= {arXiv preprint arXiv:math/0012082},
year = {2007}
}
Comments
18 pages. Proof of Proposition 2.5 corrected and related examples included (the irrelevant ideal does not necessarily commute with base change, but its radical does)