 

Charles Vial
Projectors on the intermediate algebraic Jacobians view print


Published: 
November 7, 2013 
Keywords: 
ChowKünneth decomposition, Kimura finitedimensionality, motives, projectors 
Subject: 
14C15, 14C25 


Abstract
Let X be a complex smooth projective variety of dimension d.
Under some assumptions on the cohomology of X, we construct
mutually orthogonal idempotents in CH_{d}(X × X) ⊗ Q
whose action on algebraically trivial cycles coincides with the
AbelJacobi map. Such a construction generalizes Murre's
construction of the Albanese and Picard idempotents and makes it
possible to give new examples of varieties admitting a selfdual
ChowKünneth decomposition as well as new examples of varieties having a Kimura
finitedimensional Chow motive. For instance, we prove that
fourfolds with Chow group of zerocycles supported on a curve (e.g.,
rationally connected fourfolds) have a selfdual ChowKünneth
decomposition. We also prove that
hypersurfaces of very low degree are Kimura finitedimensional.


Acknowledgements
This work was supported by a Nevile Research Fellowship at Magdalene College, Cambridge and an EPSRC Postdoctoral Fellowship under grant EP/H028870/1. I would like to thank both institutions for their support.


Author information
DPMMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK
C.Vial@dpmms.cam.ac.uk

