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Sporadic cycles on CM abelian varieties. (English) Zbl 0798.14025
The paper gives an example of an abelian variety with the following two properties:
(i) The Mumford-Tate group is not maximal.
(ii) The ring of Hodge cycles is generated by classes of divisors.

MSC:
14K22 Complex multiplication and abelian varieties
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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References:
[1] P. Deligne : Hodge cycles on abelian varieties (notes by J. S. Milne) . Lecture Notes in Mathematics 900 (1982), 9-100. · Zbl 0537.14006
[2] H. Pohlmann : Algebraic cycles on abelian varieties of complex multiplication type . Ann. Math. 88 (1968), 161-180. · Zbl 0201.23201
[3] K. Ribet : Hodge classes on certain types of abelian varieties . Am. J. Math. 105 (1983), 523-535. · Zbl 0586.14003
[4] J. Serre : Abelian l-adic Representations and Elliptic Curves . McGill University lecture notes, with William Kuyk and John Labute, 1968. · Zbl 0902.14016
[5] G. Smith : Generic Cyclic Polynomials and Some Applications . Ph.D. thesis, 1990.
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