Hasse principles for multinorm equations

Abstract

Let $k$ be a global field and let $L_0$,...,$L_m$ be finite separable field extensions of $k$. In this paper, we are interested in the Hasse principle for the multinorm equation $\underset{i=0}{\prod ^m}{N}_{L_i/k}(t_i)=c$. Under the assumption that $L_0$ is a cyclic extension, we give an explicit description of the Brauer-Manin obstruction to the Hasse principle. We also give a complete criterion for the Hasse principle for multinorm equations to hold when $L_0$ is a meta-cyclic extension.

Add an assumption to Prop. 5.13, Prop. 5.14 and Thm. 8.1