On algebraic isomorphisms of cohomology of a compactification of the Néron model with multiplications from an imaginary quadratic field

It is proved that the Grothendieck standard conjecture of Lefschetz type holds for rational cohomology of degrees 2, 3 of a Künnemann compactification of the Néron minimal model of an absolutely simple principally polarized Abelian variety of non-exceptional dimension divisible by 4 over the field of rational functions of a smooth projective curve provided that the ring of endomorphisms of the generic geometric fibre is an order of an imaginary quadratic field.