Chai's additivity conjecture for base change conductors

Let $G^\bullet:0\to T\to B\to A\to 0$ be an exact sequence of semiabelian varieties over $K$. Let $\mathscr{G}^\bullet:0\to\mathscr{T}\to\mathscr{B}\to\mathscr{A}\to 0$ be the associated complex of Néron lft-models over $\mathcal{O}_K$, with $\mathscr{T}$ in degree $1$. For a finite separable extension $L/K$ over which $T$, $B$, and $A$ acquire semiabelian reduction, define

$$c(B):=\frac{1}{[L:K]}\ell_{\mathcal{O}_L}\!\left(\operatorname{coker}\!\left(\operatorname{Lie}\mathscr{B}\otimes_{\mathcal{O}_K}\mathcal{O}_L\to\operatorname{Lie}\mathscr{B}_L\right)\right),$$

and similarly define $c(T)$ and $c(A)$.

Chai's additivity conjecture. Assume that $T$ is a torus and that $A$ is an Abelian variety. Then

$$c(B)=c(T)+c(A).$$

This is the additivity property for base change conductors in an exact sequence of semiabelian varieties. The supplied text attributes the statement to Chai but gives no information about whether it has been proved or remains open.