A note on asymptotically good extensions in which infinitely many primes split completely (Q2203987)

Let \(p\) be a prime number, and let \(K\) be a number field. For \( p = 2\), the authors assume moreover that \(K\) is totally imaginary. In this paper, which is inspired by a recent work of \textit{F. Hajir} et al. [Adv. Math. 373, Article ID 107318, 8 p. (2020; Zbl 1469.11440)], the authors prove the existence of asymptotically good extensions \(L/K\) of cohomological dimension \(2\) in which infinitely many primes split completely.