Smoothness of equivariant derived categories
K-Theory and Homology
2018-05-16 v3 Algebraic Geometry
Representation Theory
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.
Cite
@article{arxiv.1205.3132,
title = {Smoothness of equivariant derived categories},
author = {Valery A. Lunts and Olaf M. Schnürer},
journal= {arXiv preprint arXiv:1205.3132},
year = {2018}
}
Comments
64 pages, Remark 4.7 improved