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Auslander-Reiten sequences on schemes

Peter Jorgensen
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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.

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Peter Jorgensen. 2003-08-05. Auslander-Reiten sequences on schemes. https://arxiv.org/abs/math/0308037

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