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

摘要

Let p be a prime number, and let K be a number field. For p = 2, assume moreover that K is totally imaginary. In this note, we prove the existence of asymptotically good extensions L/K of cohomological dimension 2 in which infinitely many primes split completely. Our result is inspired by a recent work of Hajir, Maire, and Ramakrishna.