Question

Why are de Rham and Hodge cohomology groups coherent if the underlying morphism is proper?

score 72 · Answer 1 · 2021-02-16 19:44:20

72

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Why are de Rham and Hodge cohomology groups coherent if the underlying morphism is proper?

Published on 16 Feb 2021 - 19:44

score 102 · Answer 2 · 2021-02-18 12:24:57

102

Views

de Rham and Hodge cohomologies become locally free after localization?

Published on 18 Feb 2021 - 12:24

score 160 · Answer 3 · 2026-03-26 16:26:42

160

Views

Quasi-coherent sheaf which is a vector bundle on curves.

Published on 26 Mar 2026 - 16:26

score 154 · Answer 4 · 2021-02-24 20:42:34

154

Views

Hodge star operator and "Serre duality"

Published on 24 Feb 2021 - 20:42

score 417 · Answer 5 · 2021-03-02 03:53:00

417

Views

Derived hom-tensor adjunction for $O_X$-modules

Published on 02 Mar 2021 - 3:53

score 143 · Answer 6 · 2026-03-22 01:35:26

143

Views

Quasi Coherent and Coherent sheaves on formal schemes.

Published on 22 Mar 2026 - 1:35

score 735 · Answer 7 · 2021-03-30 20:46:21

735

Views

Some questions concerning reflexive and saturated sheaves

Published on 30 Mar 2021 - 20:46

score 129 · Answer 8 · 2021-04-06 10:34:40

129

Views

Contradiction with "cohomology group of coherent sheaf of module on projective scheme over field is finite dimensional"

Published on 06 Apr 2021 - 10:34

score 32 · Answer 9 · 2021-04-10 21:16:41

32

Views

Semi-continuity theorem and construction of Hilbert and Quot schemes

Published on 10 Apr 2021 - 21:16

score 49 · Answer 10 · 2021-05-17 14:19:48

49

Views

Locally freeness inherited on nice subsheaves?

Published on 17 May 2021 - 14:19

score 561 · Answer 11 · 2021-05-25 13:40:21

561

Views

Ideal sheaf of a point in $\mathbb{P}^1$

Published on 25 May 2021 - 13:40

score 37 · Answer 12 · 2021-05-31 21:49:53

37

Views

Resolving a coherent sheaf $\mathcal F$ over $\mathbb P^n_S$ via sheafs of the form $\oplus^p\mathcal O_{\mathbb P^n_S}(n)$, where $S$ is Noeth., aff.

Published on 31 May 2021 - 21:49

score 132 · Answer 13 · 2021-06-01 09:24:16

132

Views

Example of a sheaf without locally free resolution

Published on 01 Jun 2021 - 9:24

score 148 · Answer 14 · 2021-06-05 21:56:50

148

Views

What is the difference between the Grothendieck and the Čech cohomology?

Published on 05 Jun 2021 - 21:56

score 77 · Answer 15 · 2021-06-10 21:21:17

77

Views

Why does $R^{1}\pi_{S*}\mathcal{F}(r)$ vanish for large-enough $r$ if $\mathcal{F}$ is coherent?

Published on 10 Jun 2021 - 21:21

List Question

Why are de Rham and Hodge cohomology groups coherent if the underlying morphism is proper?

de Rham and Hodge cohomologies become locally free after localization?

Quasi-coherent sheaf which is a vector bundle on curves.

Hodge star operator and "Serre duality"

Derived hom-tensor adjunction for $O_X$-modules

Quasi Coherent and Coherent sheaves on formal schemes.

Some questions concerning reflexive and saturated sheaves

Contradiction with "cohomology group of coherent sheaf of module on projective scheme over field is finite dimensional"

Semi-continuity theorem and construction of Hilbert and Quot schemes

Locally freeness inherited on nice subsheaves?

Ideal sheaf of a point in $\mathbb{P}^1$

Resolving a coherent sheaf $\mathcal F$ over $\mathbb P^n_S$ via sheafs of the form $\oplus^p\mathcal O_{\mathbb P^n_S}(n)$, where $S$ is Noeth., aff.

Example of a sheaf without locally free resolution

What is the difference between the Grothendieck and the Čech cohomology?

Why does $R^{1}\pi_{S*}\mathcal{F}(r)$ vanish for large-enough $r$ if $\mathcal{F}$ is coherent?

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