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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.

1 vote
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A question about minimal system of generators and regular sequences

Let $(R,\mathfrak{m},k)$ a Noetherian local ring and $I$ an ideal. Suppose that: $\mu(I)=\operatorname{grade}(I,R)+1$ and $\operatorname{pd}_R(R/I)=\operatorname{grade}(I,R)$. (Some people says $I$ is …
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2 votes
1 answer
289 views

A question about mapping cone and resolutions

I am studying this papper https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-44/issue-3/Betti-numbers-of-almost-complete-intersections/10.1215/ijm/1256060413.full By Daniel Dugg …
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