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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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Vectorial extensions of abelian varities
Hi,
this is a very vague question, but I'm also glad about vague answers...
One knows that for an abelian variety over the complex numbers, one has a canonical exact sequence
$0\rightarrow \Omega^1 …