Nilpotence and generation in the stable module category

David J. Benson, Jon F. Carlson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Nilpotence has been studied in stable homotopy theory and algebraic geometry. We study the corresponding notion in modular representation theory of finite groups, and apply the discussion to the study of ghosts, and generation of the stable module category. In particular, we show that for a finitely generated kG-module M, the tensor M-generation number and the tensor M-ghost number are both equal to the degree of tensor nilpotence of a certain map associated with M.

Original languageEnglish
Pages (from-to)3566-3584
Number of pages19
JournalJournal of Pure and Applied Algebra
Issue number11
Early online date8 Feb 2018
Publication statusPublished - 30 Nov 2018


  • Nilpotence
  • homotopy
  • algebraic geometry


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