The essential cover and the absolute cover of a schematic space

Wolfgang Rump, and Yi Chuan Yang. "The essential cover and the absolute cover of a schematic space." Colloquium Mathematicae 114.1 (2009): 53-75. <http://eudml.org/doc/283750>.

@article{WolfgangRump2009,
abstract = {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.},
author = {Wolfgang Rump, Yi Chuan Yang},
journal = {Colloquium Mathematicae},
keywords = {schematic space; spectral space; Stone space; essential cover},
language = {eng},
number = {1},
pages = {53-75},
title = {The essential cover and the absolute cover of a schematic space},
url = {http://eudml.org/doc/283750},
volume = {114},
year = {2009},
}

TY - JOUR
AU - Wolfgang Rump
AU - Yi Chuan Yang
TI - The essential cover and the absolute cover of a schematic space
JO - Colloquium Mathematicae
PY - 2009
VL - 114
IS - 1
SP - 53
EP - 75
AB - 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.
LA - eng
KW - schematic space; spectral space; Stone space; essential cover
UR - http://eudml.org/doc/283750
ER -