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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Self-tilting complexes yield unstable modules
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by Alexander Zimmermann PDF
Trans. Amer. Math. Soc. 354 (2002), 2707-2724 Request permission


Let $G$ be a group and $R$ a commutative ring. Let $TrPic_R(RG)$ be the group of isomorphism classes of standard self-equivalences of the derived category of bounded complexes of $RG$-modules. The subgroup $HD_R(G)$ of $TrPic_R(RG)$ consisting of self-equivalences fixing the trivial $RG$-module acts on the cohomology ring $H^*(G,R)$. The action is functorial with respect to $R$. The self-equivalences which are ’splendid’ in a sense defined by J. Rickard act naturally with respect to transfer and restriction to centralizers of $p$-subgroups in case $R$ is a field of characteristic $p$. In the present paper we prove that this action of self-equivalences on $H^*(G,R)$ commutes with the action of the Steenrod algebra, and study the behaviour of the action of splendid self-equivalences with respect to Lannes’ $T$-functor.
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Additional Information
  • Alexander Zimmermann
  • Affiliation: Faculté de Mathématiques et CNRS (LAMFA FRE 2270), Université de Picardie, 33 rue St Leu, 80039 Amiens Cedex, France
  • MR Author ID: 326742
  • Email:
  • Received by editor(s): August 28, 2001
  • Published electronically: February 25, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2707-2724
  • MSC (2000): Primary 16E30, 20J06, 55S10, 18E30
  • DOI:
  • MathSciNet review: 1895199