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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.

2 votes
1 answer
617 views

Torsion free quasi-coherent sheaves

Let $R$ be an integral domain and $M$ be a torsion free injective module. Then $M$ is of the form $\oplus_{I}K$ (for some index set $I$), where $K$ is the quotient field of $R$. Now let $\cal F$ be a …