On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci

We prove that the Grothendieck standard conjecture $B(X)$ of Lefschetz type on the algebraicity of the operator ${}^{\mathrm{c}}\Lambda$ of Hodge theory is true for the fibre product $X=X_1\times_CX_2\times_CX_3$ of complex elliptic surfaces $X_k\to C$ over a smooth projective curve $C$ provided that the discriminant loci $\{\delta\in C\mid \operatorname{Sing}(X_{k\delta})\neq \varnothing\}$ $(k=1,2,3)$ are pairwise disjoint.