List questions from homological-algebra

Published on 10 May 2026 - 14:29

309

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Computing the Grothendieck group of a polynomial ring (over a field) or affine n-space as a scheme?

Published on 10 May 2026 - 15:48

1k

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Change of rings for $\mathrm{Ext}$ and $\mathrm{Tor}$ functors.

Published on 14 Apr 2026 - 2:36

144

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Linear Algebra for Khovanov Homology

Published on 10 May 2026 - 16:12

409

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Any module over a regular local ring has finite free resolution

Published on 10 May 2026 - 21:10

89

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Dualizing cochain complex and Hochschild complex

Published on 13 May 2026 - 11:41

43

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No projective sheaves on affine real space

Published on 10 May 2026 - 17:36

418

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Equivalence between exactness of additive functors

Published on 10 May 2026 - 15:45

154

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$HH_1(\mathbb{C})=0$ over $\mathbb{C}$, but $HH_1(\mathbb{C})\neq 0$ over $\mathbb{Q}$

Published on 15 Apr 2026 - 16:58

100

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Homology shows $\mathbb Z\cong 0$?

Published on 12 Apr 2026 - 14:45

75

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Example of coherent ring with finite self FP-Injective dimension

Published on 14 Apr 2026 - 0:17

124

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Cohomological proof of Wedderburn's theorem on the finite division algebra

Published on 10 May 2026 - 8:43

277

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Isomorphism in a commutative diagram, variation of snake lemma

Published on 17 Apr 2026 - 2:27

262

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Why $\mathrm{Ext}^n_{R[t]}(X, Y)\simeq\mathrm{Ext}^n_R(X, Y)\oplus\mathrm{Ext}^{n-1}_R(X, Y)$?

Published on 10 May 2026 - 14:32

889

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Kernel of chain map in $\textbf{Ch}(\mathcal{A})$ with $\mathcal{A}$ an abelian category (Weibel 1.2.3)

Published on 16 Apr 2026 - 0:50

List Question

Homology as a Derived Functor

Computing the Grothendieck group of a polynomial ring (over a field) or affine n-space as a scheme?

Change of rings for $\mathrm{Ext}$ and $\mathrm{Tor}$ functors.

Linear Algebra for Khovanov Homology

Any module over a regular local ring has finite free resolution

Dualizing cochain complex and Hochschild complex

No projective sheaves on affine real space

Equivalence between exactness of additive functors

$HH_1(\mathbb{C})=0$ over $\mathbb{C}$, but $HH_1(\mathbb{C})\neq 0$ over $\mathbb{Q}$

Homology shows $\mathbb Z\cong 0$?

Example of coherent ring with finite self FP-Injective dimension

Cohomological proof of Wedderburn's theorem on the finite division algebra

Isomorphism in a commutative diagram, variation of snake lemma

Why $\mathrm{Ext}^n_{R[t]}(X, Y)\simeq\mathrm{Ext}^n_R(X, Y)\oplus\mathrm{Ext}^{n-1}_R(X, Y)$?

Kernel of chain map in $\textbf{Ch}(\mathcal{A})$ with $\mathcal{A}$ an abelian category (Weibel 1.2.3)

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