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Abelian varieties and the general Hodge conjecture

Published online by Cambridge University Press:  04 December 2007

SALMAN ABDULALI
SALMAN ABDULALI
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA e-mail: [email protected] Department of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A.
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Abstract

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We investigate the relationship between the usual and general Hodge conjectures for abelian varieties. For certain abelian varieties $A$, we show that the usual Hodge conjecture for all powers of $A$ implies the general Hodge conjecture for $A$.

Keywords

Hodge conjecturealgebraic cycleabelian varietyKuga fiber variety
Type
Research Article
Information
Compositio Mathematica , Volume 109 , Issue 3 , December 1997 , pp. 341 - 355
Copyright
© 1997 Kluwer Academic Publishers