A NOTE ON ASYMPTOTICALLY GOOD EXTENSIONS IN WHICH INFINITELY MANY PRIMES SPLIT COMPLETELY

Oussama Hamza (1) , Christian Maire (2)

1 ENS de Lyon - École normale supérieure de Lyon
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

Let p be a prime number, and let K be a number field. For p=2, assume moreover K 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 [7].

Domains: Number Theory [math.NT]

Oussama Hamza, Christian Maire. A NOTE ON ASYMPTOTICALLY GOOD EXTENSIONS IN WHICH INFINITELY MANY PRIMES SPLIT COMPLETELY. 2020. ⟨hal-02489967⟩