Rigid Dualizing Complexes via Differential Graded Algebras (Survey)

Details Rigid Dualizing Complexes via Differential Graded Algebras (Survey) Rigid Dualizing Complexes via Differential Graded Algebras (Survey)

2007-09-13

arxiv.org/abs/0709.2149v2

Mathematics

Algebraic Geometry

9 pages, minor changes, final version (to appear proc. Conf. Triangulated Categories, Leeds 2006)

Scientific paper

In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their functorial properties. Due to the possible presence of torsion, we must use differential graded algebras in the constructions. We then discuss rigid dualizing complexes. Finally we show how rigid complexes can be used to understand Cohen-Macaulay homomorphisms and relative dualizing sheaves.

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