Lemma 21.4.2 (03AI)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 21: Cohomology on Sites
Section 21.4: First cohomology and torsors
Lemma 21.4.2 (cite)

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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 April 17, 2018 at 07:46

There should be a space before $\Gamma$

Comment #3358 by Johan on May 19, 2018 at 16:50

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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