How does one go about computing the cohomology groups $H^*(\mathrm{GL}_{\kern{0.1em}{m}}(\overline{\mathbb{F}}_p),M)$? I am particularly interested in the case when $M$ is an algebraic representation. I would also like to avoid assuming that $p$ is very big compared to $m$. One example of interest: $M$ is the adjoint representation of dimension $m^2$.
2026-03-28 22:31:12.1774737072
The cohomology of $\mathrm{GL}_n$ over an algebraically closed field
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