Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

On complexes of finite complete intersection dimension

Pages: 49 – 54

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n2.a4


Petter Andreas Bergh (Institutt for matematiske fag, NTNU, Trondheim, Norway)


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


finite complete intersection dimension; complexity; virtually small complexes

2010 Mathematics Subject Classification

18E30, 18G10

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