Ample families, multihomogeneous spectra, and algebraization of formal schemes

Holger Brenner and Stefan Schröer

Vol. 208 (2003), No. 2, 209–230

DOI: 10.2140/pjm.2003.208.209

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.

Milestones

Received: 13 April 2001

Published: 1 February 2003