6 papers · 1 filter
Local Minkowski units in non-abelian extensions with cyclic Sylow -subgroups
Wan Lee, Donghyeok Lim
We establish a criterion for the existence of a local Minkowski unit at that applies to all Galois extensions with Galois group isomorphic to the direct product of a non--gr…
Construction Of Non-Odd Galois Representations With Large Image
Donghyeok Lim, Christian Maire
In this work, we construct Galois representations with large image that are not GL r -odd (or, equivalently, not regular at infinity). More precisely, for every prime p {\v e} 3, e…
Massey products and unipotent extensions with restricted ramification
Oussama Hamza, Donghyeok Lim, Christian Maire
We fix a prime p and construct new cases of pro-p extensions of number fields with restricted ramification and splitting, whose Galois groups decompose as coproducts of pro-p absol…
On Krull-Schmidt decompositions of unit groups of number fields
Asuka Kumon, Donghyeok Lim
We prove that the Krull-Schmidt decomposition of the Galois module of the -adic completion of algebraic units is controlled by the primes that are ramified in the Galois extensi…
On the existence of Minkowski units
David Burns, Donghyeok Lim, Christian Maire
We investigate the Galois structure of algebraic units in cyclic extensions of number fields and thereby obtain strong new results on the existence of independent Minkowski -uni…
On the analyticity of the maximal extension of a number field with prescribed ramification and splitting
Donghyeok Lim, Christian Maire
We determine all the -adic analytic groups that are realizable as Galois groups of the maximal pro- extensions of number fields with prescribed ramification and splitting und…