Question

If a resolution $f:Y\to X$ satisfies $R^if_\omega_Y=0$ and $R^if_\mathcal{O}_Y=0$ for all $i>0$, then do we have $f_*\omega_Y=\omega_X$?

score 144 · Answer 1 · 2026-03-25 12:29:22

144

Views

If a resolution $f:Y\to X$ satisfies $R^if_\omega_Y=0$ and $R^if_\mathcal{O}_Y=0$ for all $i>0$, then do we have $f_*\omega_Y=\omega_X$?

Published on 25 Mar 2026 - 12:29

score 47 · Answer 2 · 2023-07-20 11:15:47

47

Views

Derived $\mathrm{Hom}$-functors commute with finite direct products?

Published on 20 Jul 2023 - 11:15

score 23 · Answer 3 · 2023-07-26 19:32:12

23

Views

Reference for result and proof that $R(g\circ f)\cong Rg\circ Rf$ for morphisms of ringed spaces $X\xrightarrow{f}Y\xrightarrow{g}Z$

Published on 26 Jul 2023 - 19:32

score 73 · Answer 4 · 2023-08-02 04:26:49

73

Views

Compute the stalk and costalk of a pushforward of the constant sheaf

Published on 02 Aug 2023 - 4:26

score 138 · Answer 5 · 2023-08-07 07:18:37

138

Views

When is the induced representation functor exact?

Published on 07 Aug 2023 - 7:18

score 141 · Answer 6 · 2023-09-08 16:57:02

141

Views

Why is the Yoneda product sometimes called cup product?

Published on 08 Sep 2023 - 16:57

score 79 · Answer 7 · 2023-09-10 09:59:41

79

Views

Right derived functors are additive

Published on 10 Sep 2023 - 9:59

score 35 · Answer 8 · 2023-09-13 05:24:11

35

Views

Proof regarding when left exact functors are $\delta$-functors

Published on 13 Sep 2023 - 5:24

score 29 · Answer 9 · 2023-09-14 01:31:36

29

Views

How to construct $\delta^i$ morphism for right derived functors?

Published on 14 Sep 2023 - 1:31

score 79 · Answer 10 · 2026-03-25 15:42:14

79

Views

$\operatorname{Tor}^{\mathbb{Z}}_1(-,-)$ on finite abelian groups is not right exact?

Published on 25 Mar 2026 - 15:42

score 41 · Answer 11 · 2023-09-20 15:00:59

41

Views

Webeil's Intro to Homological Algebra: does theorem 10.6.3 implicitly reindex cochain complexes to chain complexes?

Published on 20 Sep 2023 - 15:00

score 55 · Answer 12 · 2023-09-27 18:55:03

55

Views

$\pi:\Bbb P^1_k\to \text{Spec}(k)$ then is $\Bbb L\pi^*\tilde{k}\cong \mathcal{O}_{\Bbb P^1_k}[0]$?

Published on 27 Sep 2023 - 18:55

score 64 · Answer 13 · 2023-10-04 15:22:38

64

Views

Why is $f_{\ast}=f_{!}$ when $f$ is proper?

Published on 04 Oct 2023 - 15:22

score 25 · Answer 14 · 2023-10-05 13:44:30

25

Views

Help studying the derived functor of the limit functor

Published on 05 Oct 2023 - 13:44

score 57 · Answer 15 · 2023-10-22 18:52:03

57

Views

Non-abelian cohomology

Published on 22 Oct 2023 - 18:52

List Question

If a resolution $f:Y\to X$ satisfies $R^if_\omega_Y=0$ and $R^if_\mathcal{O}_Y=0$ for all $i>0$, then do we have $f_*\omega_Y=\omega_X$?

Derived $\mathrm{Hom}$-functors commute with finite direct products?

Reference for result and proof that $R(g\circ f)\cong Rg\circ Rf$ for morphisms of ringed spaces $X\xrightarrow{f}Y\xrightarrow{g}Z$

Compute the stalk and costalk of a pushforward of the constant sheaf

When is the induced representation functor exact?

Why is the Yoneda product sometimes called cup product?

Right derived functors are additive

Proof regarding when left exact functors are $\delta$-functors

How to construct $\delta^i$ morphism for right derived functors?

$\operatorname{Tor}^{\mathbb{Z}}_1(-,-)$ on finite abelian groups is not right exact?

Webeil's Intro to Homological Algebra: does theorem 10.6.3 implicitly reindex cochain complexes to chain complexes?

$\pi:\Bbb P^1_k\to \text{Spec}(k)$ then is $\Bbb L\pi^*\tilde{k}\cong \mathcal{O}_{\Bbb P^1_k}[0]$?

Why is $f_{\ast}=f_{!}$ when $f$ is proper?

Help studying the derived functor of the limit functor

Non-abelian cohomology

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