Auslander-Reiten sequences on schemes
Algebraic Geometry
2007-05-23 v1 Rings and Algebras
Abstract
Let X be a smooth projective scheme of dimension d >= 1 over the field k, and let C be an indecomposable coherent sheaf on X. Then there is an Auslander-Reiten sequence in the category of quasi-coherent sheaves on X, with C as right hand end term. The left hand end term of the sequence can be computed. It is the (d-1)'st syzygy in a minimal injective resolution of C, tensor the dualizing sheaf of X.
Cite
@article{arxiv.math/0308037,
title = {Auslander-Reiten sequences on schemes},
author = {Peter Jorgensen},
journal= {arXiv preprint arXiv:math/0308037},
year = {2007}
}
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8 pages