Definition 64.19.3. Now assume that \mathcal{F} is a \mathbf{Q}_\ell -sheaf on X. In this case we define
L(X, \mathcal{F}) := \prod \nolimits _{x \in |X|} \det (1 - \pi _ x^*T^{\deg x} |_{\mathcal{F}_{\bar x}})^{-1} \in \mathbf{Q}_\ell [[T]].
Note that this product converges since there are finitely many points of a given degree. We call this the L-function of \mathcal{F}.
Comments (0)