List questions from sheaf-cohomology

514

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Let $S^1$ be the circle (with its usual topology), and let $\mathbb{Z}$ be the constant sheaf. Show that $H^1(S^1,\mathbb{Z})\cong\mathbb{Z}$.

Published on 29 May 2014 - 15:13

359

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Question on calculating hypercohomology

Published on 25 Mar 2026 - 15:32

320

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Asterisk Notation

Published on 22 Jul 2014 - 18:24

209

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Prove that $H^1(\mathcal{M}^*)=0$.

Published on 28 Jul 2014 - 22:44

108

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Analytic cohomology on Zariski site vs analytic cohomology on analytic site

Published on 30 Jul 2014 - 8:03

697

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Hypercohomology: finding a resolution for the de Rham complex of $\mathbb{CP}^1 $

Published on 03 Aug 2014 - 12:07

71

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Showing the image of $H^j(X;\mathbb C^\times)$ lies in the torsion subgroup of $H^{j+1}(X;\mathbb Z)$

Published on 20 Aug 2014 - 22:36

2.4k

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Showing Grothendieck's Vanishing Theorem provides a strict bound

Published on 27 Aug 2014 - 0:16

1.5k

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Is the constant sheaf $\mathbb{Q}$ injective?

Published on 27 Aug 2014 - 19:16

31

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Left and right module on the cohomology of a sheaf

Published on 03 Sep 2014 - 15:06

107

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Cohomology of intersection of hyperplanes

Published on 26 Oct 2014 - 16:09

199

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Computing cohomology of the sheaf $\mathcal{End}(T_{\mathbb{P}^2})$ restricted to a curve

Published on 09 Nov 2014 - 13:01

457

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Action on sheaf cohomology in Bott-Borel-Weil theorem

Published on 10 Nov 2014 - 15:25

223

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Why is $H^1(X, \mathcal{O}) \neq 0$ for $X = (B(0, 1)\times B(0, 2)) \cup (B(0, 2)\times B(0, 1))$?

Published on 10 Nov 2014 - 18:07

237

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The Theorem on Formal Funtions - Harthshorne Theorem 11.1

Published on 16 Nov 2014 - 11:09

List Question

Let $S^1$ be the circle (with its usual topology), and let $\mathbb{Z}$ be the constant sheaf. Show that $H^1(S^1,\mathbb{Z})\cong\mathbb{Z}$.

Question on calculating hypercohomology

Asterisk Notation

Prove that $H^1(\mathcal{M}^*)=0$.

Analytic cohomology on Zariski site vs analytic cohomology on analytic site

Hypercohomology: finding a resolution for the de Rham complex of $\mathbb{CP}^1 $

Showing the image of $H^j(X;\mathbb C^\times)$ lies in the torsion subgroup of $H^{j+1}(X;\mathbb Z)$

Showing Grothendieck's Vanishing Theorem provides a strict bound

Is the constant sheaf $\mathbb{Q}$ injective?

Left and right module on the cohomology of a sheaf

Cohomology of intersection of hyperplanes

Computing cohomology of the sheaf $\mathcal{End}(T_{\mathbb{P}^2})$ restricted to a curve

Action on sheaf cohomology in Bott-Borel-Weil theorem

Why is $H^1(X, \mathcal{O}) \neq 0$ for $X = (B(0, 1)\times B(0, 2)) \cup (B(0, 2)\times B(0, 1))$?

The Theorem on Formal Funtions - Harthshorne Theorem 11.1

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