Smoothness of equivariant derived categories

Abstract

We introduce the notion of (homological) G-smoothness for a complex G-variety X, where G is a connected affine algebraic group. This is based on the notion of smoothness for dg algebras and uses a suitable enhancement of the G-equivariant derived category of X. If there are only finitely many G-orbits and all stabilizers are connected, we show that X is G-smooth if and only if all orbits O satisfy H^*(O; R)=R. On the way we prove several results concerning smoothness of dg categories over a graded commutative dg ring.

64 pages, Remark 4.7 improved

References in corpus (2)

• Higher Topos Theory
• On Serre duality for compact homologically smooth DG algebras

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