\theoname 6.9.3 . [01X4]

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\theoname 6.9.3.

On conserve les notations de la proposition 6.9.2. On suppose de plus que $X$ est génériquement lisse et que le corps $k$ est stable. Alors, pour tout $x\in S$ , on a l’égalité

\lambda_{x}=\left[\mathopen{|}{{\mathscr{H}}(x)^{\times}}\mathclose{|}:\mathopen{|}{k^{\times}}\mathclose{|}\right]\int_{\widetilde{(X,x)}}\bigwedge_{j=1}^{n}c_{1}(\widetilde{\mathsf{L}_{i}}(x))