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The essential cover and the absolute cover of a schematic space

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Rump W., Yang Y.

Colloquium Mathematicum

2009

tom 114

nr 1

53-75

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Rump W.

1 Yang Y.

1 2009

Wyniki wyszukiwania

The essential cover and the absolute cover of a schematic space