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Let $X$ be a regular Noetherian scheme. I read in Milne's book on Etale Cohomology that this implies that $H^2(X_{Zar},\mathcal{O}_X^\times)=0$. Can anyone explain the proof of this fact or give a reference to the proof?

Mr. Frog
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  • Consider posting on MathOverflow for a change of getting an answer from Mline himself: https://mathoverflow.net/users/930/js-milne – Tanner Strunk Jan 23 '18 at 05:57
  • (Etale cohomology still scares me a bit...) – Tanner Strunk Jan 23 '18 at 05:58
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    https://math.stackexchange.com/questions/2610807/second-zariski-cohomology-of-the-multiplicative-group/2612039#2612039 (Note that $\mathbb{G}_m$ is just another name for $\mathcal{O}_X^{\times}$) – Johann Haas Jan 23 '18 at 09:05

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