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Results tagged with homological-algebra
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user 22873
(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.
12
votes
2
answers
447
views
When are MCM ideals principal?
Suppose $(R,\mathfrak m, k)$ is a $d$-dimensional Cohen-Macaulay local ring with canonical module $\omega_R$ and $d>1$. Suppose $I\subset R$ is an ideal which is MCM (=maximal Cohen-Macaulay, i.e., i …
- 30.5k
5
votes
Generalizing miracle flatness (Matsumura 23.1) via finite Tor-dimension
If you are willing to impose instead a condition on the closed fiber, namely, that it be regular, then you only need to assume something like $A$ being an excellent normal domain with perfect residue …
- 558