\title[A local-global principle for small triangulated categories]{A
  local-global principle\\ for small triangulated categories}

\author[Benson, Iyengar, Krause]{Dave Benson, Srikanth B. Iyengar, Henning Krause}

\address{Dave Benson \\ 
Institute of Mathematics\\ 
University of Aberdeen\\ 
King's College\\ 
Aberdeen AB24 3UE\\ 
Scotland U.K.}

\address{Srikanth B. Iyengar\\ 
Department of Mathematics\\
University of Nebraska\\ 
Lincoln, NE 68588\\ 
U.S.A.}

\address{Henning Krause\\ 
Fakult\"at f\"ur Mathematik\\ 
Universit\"at Bielefeld\\ 
33501 Bielefeld\\ 
Germany.}

%%%%%%%%%%%%% end header

\begin{document}

\begin{abstract}
  Local cohomology functors are constructed for the category of
  cohomological functors on an essentially small triangulated category
  $\sfT$ equipped with an action of a commutative noetherian
  ring. This is used to establish a local-global principle and to
  develop a notion of stratification, for $\sfT$ and the cohomological
  functors on it, analogous to such concepts for compactly generated
  triangulated categories.
\end{abstract}

\keywords{cohomological functor, local cohomology, local-global principle, support}
\subjclass[2010]{18E30 (primary), 13D45, 16E35, 20J06}

\thanks{Version from May 7, 2013.\\
  The authors are grateful to MSRI at Berkeley for support while this
  work was in progress.  The second author was partly supported by NSF
  grant DMS 1201889 and a Simons Fellowship.}