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Rigid dualizing complexes via differential graded algebras (survey). (English) Zbl 1211.18010
Holm, Thorsten (ed.) et al., Triangulated categories. Based on a workshop, Leeds, UK, August 2006. Cambridge: Cambridge University Press (ISBN 978-0-521-74431-7/pbk). London Mathematical Society Lecture Note Series 375, 452-463 (2010).
Summary: 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.
For the entire collection see [Zbl 1195.18001].

MSC:
18E30 Derived categories, triangulated categories (MSC2010)
18G10 Resolutions; derived functors (category-theoretic aspects)
16E45 Differential graded algebras and applications (associative algebraic aspects)
18G15 Ext and Tor, generalizations, K√ľnneth formula (category-theoretic aspects)
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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