A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full subcategory of extremally disconnected spaces. Such a cover of a space is called its absolute. We prove that the absolute exists within the category of schematic spaces, i.e. the spaces underlying a scheme. For a schematic space, we use the absolute to generalize Bourbaki's concept of irreducible component, so that embedded and multiple components may arise. We introduce the essential cover of a schematic space, and show that it parametrizes the generalized components.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-6,
author = {Wolfgang Rump and Yi Chuan Yang},
title = {The essential cover and the absolute cover of a schematic space},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {53-75},
zbl = {1166.54002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-6}
}
Wolfgang Rump; Yi Chuan Yang. The essential cover and the absolute cover of a schematic space. Colloquium Mathematicae, Tome 116 (2009) pp. 53-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-6/