36 research outputs found
Zero-cycles on varieties over p-adic fields and Brauer groups
In this paper, we study the Brauer-Manin pairing of smooth proper varieties
over local fields, and determine the -adic part of the kernel of one side.
We also compute the of a potentially rational surface which splits over a
wildly ramified extension.Comment: 31 pages. The proof of the main result in the local case has been
much simplified. The computations of 0-cycles on cubic surfaces have been
modifie
Torsion birational motives of surfaces and unramified cohomology
Let and be smooth projective varieties over an algebraically closed
field. Suppose that is a surface admitting a decomposition of the diagonal.
We show that, away from the characteristic of , if an algebraic
correspondence acts trivially on the unramified cohomology, then it
acts trivially on any normalized, birational, and motivic functor. This
generalizes Kahn's result on the torsion order of . We also exhibit an
example of over for which violates the integral
Hodge conjecture.Comment: 25 page