hal-01413224
https://u-bourgogne.hal.science/hal-01413224
arxiv:1310.2782
doi:10.1007/s00229-015-0783-1
[UNIV-BOURGOGNE] Université de Bourgogne
[CNRS] CNRS - Centre national de la recherche scientifique
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[IMB_UMR5584] Institut de Mathématiques de Bourgogne
Motives of quadric bundles
Bouali, Johann
[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]
ART
This article is about motives of quadric bundles. In the case of odd dimensional fibers and where the basis is of dimension two we give an explicit relative Chow–Künneth decomposition. This relative Chow–Künneth decomposition shows that the motive of the quadric bundle is isomorphic to the direct sum of Tate twists of the motive of the base and of the Prym motive of a double cover of the discriminant. In particular this is a refinement with Q—coefficients of a result of Beauville concerning the cohomology and the Chow groups of an odd dimensional quadric bundle over P2. This relative Chow–Künneth decomposition induces an absolute Chow–Künneth decomposition which satisfies parts of Murre’s conjectures. This article is a generalization of an article of Nagel and Saito on conic bundles (Nagel and Saito in Int Math Res Not IMRN 16, 2978–3001, 2009).
2016-03
en
Manuscripta mathematica
Springer Verlag