## Rocky Mountain Journal of Mathematics

### Affine ringed spaces and Serre's criterion

#### 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.

#### Article information

Source
Rocky Mountain J. Math., Volume 47, Number 6 (2017), 2051-2081.

Dates
First available in Project Euclid: 21 November 2017

https://projecteuclid.org/euclid.rmjm/1511254964

Digital Object Identifier
doi:10.1216/RMJ-2017-47-6-2051

Mathematical Reviews number (MathSciNet)
MR3725256

Zentralblatt MATH identifier
06816582

#### Citation

Salas, Fernando Sancho de; Salas, Pedro Sancho de. Affine ringed spaces and Serre's criterion. Rocky Mountain J. Math. 47 (2017), no. 6, 2051--2081. doi:10.1216/RMJ-2017-47-6-2051. https://projecteuclid.org/euclid.rmjm/1511254964

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