Hasse principles for multinorm equations

摘要

Let $k$ be a global field and let $L_0$,...,$L_m$ be finite separable fieldextensions of $k$. In this paper, we are interested in the Hasse principle forthe multinorm equation $underset{i=0}{overset{m}{prod}}N_{L_i/k}(t_i)=c$.Under the assumption that $L_0$ is a cyclic extension, we give an explicitdescription of the Brauer-Manin obstruction to the Hasse principle. We alsogive a complete criterion for the Hasse principle for multinorm equations tohold when $L_0$ is a meta-cyclic extension.