On the equation N_K/k(Ξ)=P(t)

2012/02/18 by Wei, Dasheng
#11G35 #14G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1202.4115

Abstract

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 polynomial, three topics have been investigated: (1) computation of the unramified Brauer group of such varieties over arbitrary fields; (2) rational points and Brauer-Manin obstruction over number fields (under Schinzel's hypothesis); (3) 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).

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