White, Samuel P. Sporadic cycles on CM abelian varieties. (English) Zbl 0798.14025 Compos. Math. 88, No. 2, 123-142 (1993). 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. Reviewer: S.P.White (Minneapolis) Cited in 6 Documents MSC: 14K22 Complex multiplication and abelian varieties 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) Keywords:abelian variety; Mumford-Tate group; ring of Hodge cycles PDF BibTeX XML Cite \textit{S. P. White}, Compos. Math. 88, No. 2, 123--142 (1993; Zbl 0798.14025) Full Text: Numdam EuDML OpenURL 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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.