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Algebraic cycles on abelian varieties and their decomposition

Giambattista Marini (2004)

Bollettino dell'Unione Matematica Italiana

For an Abelian Variety X , the Künneth decomposition of the rational equivalence class of the diagonal Δ X × X gives rise to explicit formulas for the projectors associated to Beauville's decomposition (1) of the Chow ring C H X , in terms of push-forward and pull-back of m -multiplication. We obtain a few simplifications of such formulas, see theorem (4) below, and some related results, see proposition (9) below.

Algebraic equivalence of real algebraic cycles

Miguel Abánades, Wojciech Kucharz (1999)

Annales de l'institut Fourier

Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.

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