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Results tagged with homological-algebra
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user 483326
(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
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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 …
- 10.7k
1
vote
0
answers
127
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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 …
- 33