The finitude of tamely ramified pro-\(p\) extensions of number fields with cyclic \(p\)-class groups

DOI10.1016/j.jnt.2024.01.005arXiv2402.08512OpenAlexW4391953171MaRDI QIDQ6150391

Donghyeok Lim, Yoon-Jin Lee

Publication date: 6 March 2024

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2402.08512

zbMATH Keywords

ray class field towerpowerful pro-\(p\) groupstame Fontaine-Mazur conjecture

Mathematics Subject Classification ID

Galois theory (11R32) Class field theory (11R37)

Cites Work

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• A note on the group of units of an algebraic number field
• Representations of cyclic groups in rings of integers. I
• Some cases of the Fontaine-Mazur conjecture
• Some cases of the Fontaine-Mazur conjecture. II
• The theory of finite groups. An introduction.
• Unramified subextensions of ray class towers
• Explicit computation of Galois \(p\)-groups unramified at \(p\)
• Finiteness of \(T\)-tamely ramified and \(S\)-decomposed towers and \(p\)-towers
• Powerfully solvable and powerfully simple groups
• Construction of maximal unramified \(p\)-extensions with prescribed Galois groups
• Some new evidence for the Fontaine-Mazur conjecture
• \(p\)-adic analytic groups
• Base change for Stark-type conjectures "over \mathbb{Z}"
• Analytic lie extensions of number fields with cyclic fixed points and tame ramification
• l-Erweiterungen mit vorgegebenen Verzweigungsstellen.
• On the \(\mathbb Z_l\)-rank of Abelian extensions with restricted ramification