2014/07/16 by Dasheng Wei · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Polynomial and algebraic computation
paper · doi:10.1112/plms/pdu035
For varieties given by an equation N K / k ( Ξ ) = P ( t ) , where N K / k is the norm form attached to a field extension K / k and P ( t ) in k [ t ] is a non-zero polynomial, three topics have been investigated: computation of the unramified Brauer group of such varieties over arbitrary fields; rational points and Brauer–Manin obstruction over number fields (under Schinzel's hypothesis); zero-cycles and Brauer–Manin obstruction over number fields. In this paper, we produce new results in each of three directions. We obtain quite general results under the assumption that K / k is abelian (as opposed to cyclic in earlier investigation).