Algebraic cycles on nonsimple abelian varieties
For an abelian variety A defined over \({\mathbb{C}}\) let Hg(A) denote the Hodge group of A, then A is stably non-degenerate if and only if the rank of \(Hg(A)_{{\mathbb{C}}}\) is equal to the reduced dimension of A [cf. the author, J. Fac. Sci., Univ. Tokyo, Sect. I A 31, 487-520 (1984; Zbl 0591.14006)]. In this paper the author proves the following: Let A, B be stably non-degenerate abelian varieties defined over \({\mathbb{C}}\) such that they have no simple component of type IV [for definition see \textit{D. Mumford}, ``Abelian varieties'', Tata Inst. Fundament. Res. Stud. Math. 5 (1970; Zbl 0223.14022 ); p. 202]. Then the product \(A\times B\) is also stably non-degenerate.
scientific article; zbMATH DE number 4142205
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