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Results tagged with homological-algebra
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user 78824
(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.
16
votes
1
answer
2k
views
Where am I suppose to actually learn how to compute hypercohomology?
I'm reading about algebraic de Rham cohomology over characteristic zero which is constructed using hypercohomology. Already, constructing injective resolutions is difficult, and coupling this with fin …
- 1,716
4
votes
0
answers
226
views
Is there an analogue to the koszul complex for constructible sheaves?
Given a variety $X$ and a complete-intersection morphism
$$
Y \to X
$$
is there an analogue of the Koszul complex for $\mathcal{O}_Y \in \textbf{Coh}(X)$ in the setting of constructible sheaves? Meani …
- 1,716
0
votes
1
answer
322
views
How can I show flatness for projective morphisms?
Are there any homological checks I can use to check if a projective morphism is flat? For example, I would expect the following projective morphism to be flat
$$
\textbf{Proj}\left( \frac{\mathbb{C}[s …
- 1,716