Abelian Log Fundamental Group scheme

Let $S$ be a connected Dedekind scheme and $X$ be a proper smooth connected scheme over $S$ . Let $D$ a divisor with no multiplicity of $X$ such that the irreducible components of $D$ and as well their intersections are smooth over $S$. Now if we endow $X$ with the log structure associated with $D$ then the structure morphism from $X$ to $S$ is log-smooth. Let $x:S\to X$ be a $S$-point such that it doesn’t intersect $D$. Then we prove that the maximal abelian quotient of the log Nori fundamental group scheme of $X$ fits in to an exact sequence of the form $0 \rightarrow ($\mathbf{N}\mathbf{S}$^{\tau}{X/S,D})^{\vee} \rightarrow (\pi^$\text{log}${$\text{Nori}$}(X,x))^{$\text{ab}$} \rightarrow \underset{n}{\varprojlim} $\mathbf{A}\mathbf{l}\mathbf{b}${X/S,D}[n] \rightarrow 0$\mathrm{.}Here$$\mathbf{N}\mathbf{S}$^{\tau}{X/S,D}$ is the torsion subgroup scheme of the generalized Neron-Severi group and ${\mathbf{A}\mathbf{l}\mathbf{b}}_{X\mathrm{/}S,D}$ is the generalized Albanese scheme associated with the divisor $D$.