Ample families, multihomogeneous spectra, and algebraization of formal schemes

Details Ample families, multihomogeneous spectra, and algebraization of formal schemes Ample families, multihomogeneous spectra, and algebraization of formal schemes

2000-12-11

arxiv.org/abs/math/0012082v3

Pacific J. Math. 208 (2003), 209-230

Mathematics

Algebraic Geometry

18 pages. Proof of Proposition 2.5 corrected and related examples included (the irrelevant ideal does not necessarily commute

Scientific paper

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.

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