Let $X,Y$ be two schemes and $f : X \to Y$ be a finite flat map. In the following document page 20, the author talks about the norm map $$f_* : f_*\mathbf{G}_{m,X} \to \mathbf{G}_{m,Y}.$$ He then says that this induces a pusch-forward of $\mathbf{G}_{m}$-torsors and a map $Pic(X) \to Pic(Y)$.
How does one define the norm map that he talks about ?
When he says that this defines a push-forward of $\mathbf{G}_{m}$-torsors is just by using the norm map locally ?
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$\begingroup$May I assume $Y$ noetherian and connected or some other hypotheses so that things work well or this is in fact your question? Then take a look to Lemma 30.14.5. in the Stacks Project:
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