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(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
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mod p (odd) cohomology of dihedral groups
I've been trying to find the cohomology for the trivial module for $\operatorname{PSL}_2(r^n)$ over $\mathbb{F}_p$ for $2 \neq p \neq r$ and have managed to reduce this to the cohomology of a maximal …