Algebraic cycles in families of abelian varieties over Hilbert-Blumenthal surfaces.
For an Abelian Variety , the Künneth decomposition of the rational equivalence class of the diagonal gives rise to explicit formulas for the projectors associated to Beauville's decomposition (1) of the Chow ring , in terms of push-forward and pull-back of -multiplication. We obtain a few simplifications of such formulas, see theorem (4) below, and some related results, see proposition (9) below.
Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.