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2017 Affine ringed spaces and Serre's criterion
Fernando Sancho de Salas, Pedro Sancho de Salas
Rocky Mountain J. Math. 47(6): 2051-2081 (2017). DOI: 10.1216/RMJ-2017-47-6-2051

Abstract

We study the notion of affine ringed space, see its meaning in topological, differentiable and algebro-geometric contexts and show how to reduce the affineness of a ringed space to that of a ringed finite space. Then, we characterize schematic finite spaces and affine schematic spaces in terms of combinatorial data. Finally, we prove Serre's criterion of affineness for schematic finite spaces. This yields, in particular, Serre's criterion of affineness on schemes.

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Fernando Sancho de Salas. Pedro Sancho de Salas. "Affine ringed spaces and Serre's criterion." Rocky Mountain J. Math. 47 (6) 2051 - 2081, 2017. https://doi.org/10.1216/RMJ-2017-47-6-2051

Information

Published: 2017
First available in Project Euclid: 21 November 2017

zbMATH: 06816582
MathSciNet: MR3725256
Digital Object Identifier: 10.1216/RMJ-2017-47-6-2051

Subjects:
Primary: 05E99, 06A11, 14A99, 14F99

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 6 • 2017
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