The $l$-part of the Tamagawa number conjecture

Let $U$ be the open arithmetic base over which the smooth $l$-adic sheaf $V_l^i$ is defined, let $T_l^i\subseteq V_l^i$ be a Galois-stable $\mathbb Z_l$-lattice, and let $\vartheta_l^i$ and $\vartheta_\infty^i$ be the comparison isomorphisms arising from the preceding conjectures. The $l$-part of the Tamagawa number conjecture. There is an identity of free rank-one $\mathbb Z_l$-submodules of $\operatorname{det}_{\mathbb Q_l}R\Gamma_c(U_{\operatorname{et}},V_l^i)$:

$$\mathbb Z_l\cdot\vartheta_l^i\circ\vartheta_\infty^i(L^*(h^i(X),0)^{-1})=\operatorname{det}_{\mathbb Z_l}R\Gamma_c(U_{\operatorname{et}},T_l^i)$$

for any Galois-stable $\mathbb Z_l$-lattice $T_l^i\subseteq V_l^i$. This is the integral $l$-adic formulation of the Tamagawa number conjecture and is independent of the chosen lattice, according to the source.