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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Zbl MR
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. 
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/
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     title = {Algebraic cycles on abelian varieties and their decomposition},
     journal = {Bollettino della Unione matematica italiana},
     pages = {231--240},
     year = {2004},
     volume = {Ser. 8, 7B},
     number = {1},
     zbl = {1112.14007},
     mrnumber = {MR2044268},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a9/}
}
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