The Stacks project

Lemma 21.4.2. Let $\mathcal{C}$ be a site. Let $\mathcal{G}$ be a sheaf of (possibly non-commutative) groups on $\mathcal{C}$. A $\mathcal{G}$-torsor $\mathcal{F}$ is trivial if and only if $\Gamma (\mathcal{C}, \mathcal{F}) \not= \emptyset $.

Proof. Omitted. $\square$

Comments (2)

Comment #3263 by Rene on

There should be a space before

Comment #3358 by on

Hmm... actually, the space is there in the latex (in the form of an end of line), but it doesn't look like it online because of the slant in the if. Looks OK in the pdf... Not fixing.

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  • 6 comment(s) on Section 21.4: First cohomology and torsors

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View Lemma 21.4.2 as pdf