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Let a connected linear algebraic group $G$ acts on an algebraic variety $X$, proper over a filed $k$.

In the proof of Proposition 1.5. of Mumford's GIT book, he says "....consider the see-saw exact sequence: $0 \rightarrow H^1(\mathcal{O}_{G}^{\times}) \rightarrow H^1(\mathcal{O}_{G\times X}^{\times}) \rightarrow H^0(G, R^1 (p_1)_{\ast} (\mathcal{O}_{G\times X}^{\times}))$". I don't know "the see-saw exact sequence" and cannot find it on the web. What is it? Where are references of it?

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    $\begingroup$ I find a lot of references when googling the title, e.g., here, page $2$. $\endgroup$ – Dietrich Burde May 31 at 8:11
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    $\begingroup$ @DietrichBurde It is "see-saw property". Are "see-saw property" and "see-saw exact sequence" same notion? $\endgroup$ – LOCOAS May 31 at 9:08

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