Dualizing Complexes and Tilting Complexes over Simple Rings

Details Dualizing Complexes and Tilting Complexes over Simple Rings Dualizing Complexes and Tilting Complexes over Simple Rings

2001-09-30

arxiv.org/abs/math/0110008v1

Mathematics

Rings and Algebras

9 pages, no figures

Scientific paper

We prove that two-sided tilting complexes, and dualizing complexes, over
simple Goldie rings (with some technical conditions) are always shifts of
invertible bimodules. This allows us to describe the derived Picard groups of
such rings, and to deduce these are Gorenstein (and sometimes even
Auslander-Gorenstein Cohen-Macaulay) rings.

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