On complexes of finite complete intersection dimension

TL;DR

This paper investigates complexes with finite complete intersection dimension in local rings, demonstrating that they generate a broad range of complexities and are virtually small, thus answering a notable open question.

Contribution

It proves that complexes of finite complete intersection dimension generate all complexities and are virtually small, advancing understanding in derived categories of local rings.

Findings

Thick subcategory contains complexes of all complexities

Such complexes are virtually small

Answers a question by Dwyer, Greenlees, and Iyengar

Abstract

We study complexes of finite complete intersection dimension in the derived category of a local ring. Given such a complex, we prove that the thick subcategory it generates contains complexes of all possible complexities. In particular, we show that such a complex is virtually small, answering a question raised by Dwyer, Greenlees and Iyengar.