Abstract
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 language | English |
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Pages (from-to) | 3566-3584 |
Number of pages | 19 |
Journal | Journal of Pure and Applied Algebra |
Volume | 222 |
Issue number | 11 |
Early online date | 8 Feb 2018 |
DOIs | |
Publication status | Published - 30 Nov 2018 |
Keywords
- Nilpotence
- homotopy
- algebraic geometry