Geodesic
Algebraic cycles on abelian varieties and their decomposition
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 231-240

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For an Abelian Variety $X$, the Künneth decomposition of the rational equivalence class of the diagonal $\Delta\subset X\times X$ gives rise to explicit formulas for the projectors associated to Beauville's decomposition (1) of the Chow ring $CH^{\bullet}(X)$, 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. 
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     author = {Marini, Giambattista},
     title = {Algebraic cycles on abelian varieties and their decomposition},
     journal = {Bollettino della Unione matematica italiana},
     pages = {231--240},
     publisher = {mathdoc},
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     year = {2004},
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     mrnumber = {MR2044268},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a9/}
}
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Marini, Giambattista. Algebraic cycles on abelian varieties and their decomposition. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 231-240. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a9/