Proposition 2.11 . [038E]

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Proposition 2.11.

Let $K^{\prime}/K$ be a finite normal extension and let $q\colon X^{\prime}:=X\otimes_{K}{K^{\prime}}\to X$ be the natural projection. For $\theta\in\mathcal{Z}^{1,1}(X)$ and $u\in C^{0}({X^{{\mathrm{an}}}})$ , we have

(2.5)

q^{*}(P_{\theta}(u))=P_{q^{*}\theta}(q^{*}(u)).