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Journal of the London Mathematical Society 2003 68(2):317-337; doi:10.1112/S0024610703004605
© 2003 by London Mathematical Society
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© The London Mathematical Society

The Brauer–Manin Obstruction for Zero-Cycles on Severi–Brauer Fibrations Over Curves

Joost van Hamel

School of Mathematics and Statistics, Carslaw Building F07, University of Sydney NSW 2006, Australia vanhamel{at}member.ams.org

Received 30 October 2002.

Introducing the framework of pseudo-motivic homology, the paper finishes the proof that the Brauer–Manin obstruction is the only obstruction to the local–global principle for zero-cycles on a Severi–Brauer fibration of squarefree index over a smooth projective curve over a number field, provided that the Tate–Shafarevich group of the Jacobian of the base curve is finite. More precisely, for such a variety the Chow group of global zero-cycles is dense in the subgroup of collections of local cycles that are orthogonal to the (cohomological) Brauer group of the variety.


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