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Mini-Workshop: Thick Subcategories - Classifications and Applications
Organized by: Ragnar-Olaf Buchweitz (1), Henning Krause (2) and Stefan Schwede (3)
(1) Department of Computer and Mathematical Sciences, University of Toronto at Scarborough, 1265 Military Trail, ON M1C 1A4, TORONTO, CANADA(2) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, BIELEFELD, GERMANY
(3) Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115, BONN, GERMANY
Thick subcategories of triangulated categories have been the main
topic of this workshop. Triangulated categories arise in many areas
of modern mathematics, for instance in algebraic geometry, in
representation theory of groups and algebras, or in stable homotopy
theory. We give three typical examples of such triangulated
categories:
\begin{itemize}
\item the category of perfect complexes of $\mathcal O_X$-modules over
a scheme $X$,
\item the stable category of finite dimensional representations of a
finite group,
\item the stable homotopy category of finite spectra.
\end{itemize}
In each case, there is a classification of thick subcategories under
some appropriate conditions. Recall that a subcategory of a
triangulated category is {\em thick}, if it is a triangulated
subcategory and closed under taking direct factors. Historically, the
first classification has been established by Hopkins and Smith for the
stable homotopy category, using the nilpotence theorem. A similar idea
was then applied by Hopkins and Neeman to categories of perfect
complexes over commutative noetherian rings. Later, Thomason extended
this classification to schemes. For stable categories of finite group
representations, the classification of thick subcategories is due to
Benson, Carlson, and Rickard.
The format of the workshop has been a combination of introductory
survey lectures and more specialized talks on recent progress and open
problems. The mix of participants from different mathematical areas
and the relatively small size of the workshop provided an ideal
atmosphere for fruitful interaction and exchange of ideas. It is a
pleasure to thank the administration and the staff of the Oberwolfach
Institute for their efficient support and hospitality.
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