Construction of a cyclic p-extension of number fields whose unit group has prescribed Galois module structure

2025/07/17 by Ozaki, Manabu
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.12949

Abstract

For any finite cyclic p-group G, we will show that every ℤ_p-torsion free finitely generated ℤ_p[G]-module appears as O_K^×⊗_ℤℤ_p up to ℤ_p[G]-free direct summands for a certain G-extension K/k of number fields.

Citations

• On Krull-Schmidt decompositions of unit groups of number fields
• On the existence of Minkowski units
• Construction of maximal unramified p-extensions with prescribed Galois groups

Related

• Galois module structure of the units modulo p^m of cyclic extensions of degree pⁿ
• Nontrivial Galois module structure of cyclotomic fields
• Galois module structure of cyclic extensions of local Fields of characteristic zero
• Little galoisian modules
• Galois Module Structure of pth-Power Classes of Extensions of Degree p