Timeline for Is the Brauer correspondence injective ?
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| Jun 8, 2012 at 21:09 | comment | added | Ralph | In the description of the Brauer correspondence (B.C.) in the question, $M$ is required to have vertex $P$ (as stated by Geoff): "... with trivial source and vertex $P$ ...". Then, of course, $\operatorname{Br}_P(M) \neq 0$, i.e. the B.C. misses $0$ as projective indecomposable $k[N_G(P)/P]$-module. This might have led to confusion. I will edit the question accordingly when I have worked through the answers. Anyway, thanks for the hint and the references. | |
| Jun 8, 2012 at 20:58 | comment | added | Geoff Robinson | But the question was about modules with vertex $P$ and trivial source wasn't it? It is certainly true that things can go wrong if you move away from indecomposable (trivial source) modules with vertex $P$. | |
| Jun 8, 2012 at 20:34 | history | answered | Natalie | CC BY-SA 3.0 |