Unramified extensions of quadratic number fields with Galois group 2.A_n

2025/05/15 by König, Joachim
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.10100

Abstract

We realize infinitely many covering groups 2.A_n (where A_n is the alternating group) as the Galois group of everywhere unramified Galois extensions over infinitely many quadratic number fields. After several predecessor works investigating special cases or proving conditional results in this direction, these are the first unramified realizations of infinitely many of these groups.

Citations

• Quadratic number fields with unramified SL₂(5)-extensions
• Unramified extensions of quadratic number fields with Galois group SL₂(7)
• On the local behaviour of specializations of function field extensions
• Specialization results and ramification conditions
• Linear Equations in Primes

Related

• Unramified alternating extensions of quadratic fields
• Unramified extensions of quadratic number fields with Galois group SL₂(7)
• Families of Unramified Extensions of Number Fields
• Quadratic number fields with unramified SL₂(5)-extensions
• Unramified extensions over low degree number fields