Chow-Künneth decomposition for universal families over Picard modular surfaces
Andrea Miller, Stefan Müller-Stach, Sigrid Wortmann, Yi-Hu Yang, and Kang Zuo
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Submission date: 14. Aug. 2006
published in: Algebraic cycles and motives : proceedings of the EAGER conference held in Leiden, August 30 - September 4, 2004. Vol. 2 / J. Nagel ... (eds.)
Cambridge : Cambridge University Press, 2007. - P. 241 - 276
(London Mathematical Society lecture note series ; 344)
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We prove existence results for Chow-Künneth projectors on compactified universal families of Abelian threefolds with complex multiplication over a particular Picard modular surface studied by Holzapfel. Our method builds up on the approach of Gordon, Hanamura and Murre in the case of Hilbert modular varieties. In addition we use relatively complete models in the sense of Mumford, Faltings and Chai and prove vanishing results for -Higgs cohomology groups of certain arithmetic subgroups in SU(2,1) which are not cocompact.