Auslander-Reiten sequences on schemes

Abstract

Auslander-Reiten sequences are the central item of Auslander-Reiten theory, which is one of the most important techniques for the investigation of the structure of abelian categories. This note considers X, a smooth projective scheme of dimension at least 1 over the field k, and C, an indecomposable coherent sheaf on X. It is proved that in the category of quasi-coherent sheaves on X, there is an Auslander-Reiten sequence ending in C. © 2006 by Institut Mittag-Leffler. All rights reserved.