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.

Locations

• Proceedings of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
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