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I am reading this article: http://arxiv.org/pdf/1310.5978.pdf. In definition 2.6 on page 4 there is claim that is made and I don't see why it is true. I will recall it here:

Let $X$ be an integral scheme and denote its function field by $K$, and $ \eta: Spec(K) \longrightarrow X$ be the generic point. Lastly, let $ M$ be a quasi coherent sheaf on $X$.

Claim: $\eta_* \eta^* (M) = M \otimes_{\mathcal{O}_{X}} \underline{K} $, where $\underline{K}$ is the constant sheaf on $X$.

Any ideas and comments would be greatly appreciated. Thanks!

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    $\begingroup$ You can do it for every open affine and then glue, because the isomorphisms are canonical. $\endgroup$
    – Lev Borisov
    Commented Feb 21, 2016 at 23:49
  • $\begingroup$ Thanks Prof. Borisov! I think I see it now, it was a stupid question :P. If you write it as an answer I will accept it. $\endgroup$
    – Rick Samuelson
    Commented Feb 22, 2016 at 9:25

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