Geodesic
On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci
Izvestiya. Mathematics , Tome 83 (2019) no. 3, pp. 613-653

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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.
Keywords: standard conjecture, resolution of indeterminacies, Clemens–Schmid sequence
Mots-clés : elliptic surface, fibre product, Gysin map. 
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     author = {S. G. Tankeev},
     title = {On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci},
     journal = {Izvestiya. Mathematics },
     pages = {613--653},
     publisher = {mathdoc},
     volume = {83},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_3_a8/}
}
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S. G. Tankeev. On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci. Izvestiya. Mathematics , Tome 83 (2019) no. 3, pp. 613-653. http://geodesic.mathdoc.fr/item/IM2_2019_83_3_a8/