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

Abstract

It is proved that the Grothendieck standard conjecture of Lefschetz type holds for rational cohomology of degrees 2, 3 of a Kunnemann compactification of the Neron 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.