2026/07/28 by Mridul Biswas, Divyasree C-Ramachandran, Biswanath Samanta
#math.NT
We study the behaviour of the Brauer--Manin obstruction to the existence of rational points under finite field extensions. For (p, mp)-normic bundles over number fields, we prove that the Brauer--Manin obstruction vanishes after base change to finite extensions whose degrees satisfy suitable p-divisibility conditions depending on m. We further show that, for (p,2p)-normic bundles with p=2 or 3, it is enough to assume that the extension degree is divisible by p. We also prove that the divisibility hypothesis is, in general optimal, by constructing a conic bundle for which the Brauer--Manin obstruction persists over a quadratic extension.