On algebraic isomorphisms of rational cohomology of a Künnemann compactification of the Néron minimal model

摘要

It is proved that the Grothendieck standard conjecture of Lefschetz type holds for rational cohomology of degree 2 or 3 of a K¨unnemann compactification of the N′eron minimal model of an absolutely simple principally polarized Abelian variety over the field of rational functions of a smooth projective curve under certain restrictions on the ring of endomorphisms of the Abelian variety.