Related papers: Sous-modules d'unit\'es en th\'eorie d'Iwasawa

In this note, we describe first the structure of minimal non-Iwasawa finite groups. Then we determine the minimal non-Iwasawa finite groups which are modular. Also, we find connections between minimal non-Iwasawa finite groups and the…

We call a unit $\beta$ in a Galois extension $l/\mathbb{Q}$ a Minkowski unit if the subgroup generated by $\beta$ and its conjugates over $\mathbb{Q}$ has maximum rank in the unit group of $l$. Minkowski showed the existence of such units…

We extend Witt's theorem to several kinds of simultaneous isometries of subspaces. We determine sufficient and necessary conditions for the extension of an isometry of subspaces $\phi:E\to E'$ to an isometry $\phi_V:V\to V'$ that also sends…

For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.

In this paper we use the Merkurjev-Suslin theorem to explore the structure of arithmetically significant Galois modules that arise from Kummer theory. Let K be a field of characteristic different from a prime \ell, n a positive integer, and…

Let $N/F$ be an odd degree Galois extension of number fields with Galois group $G$ and rings of integers ${\mathfrak O}_N$ and ${\mathfrak O}_F=\bo$ respectively. Let $\mathcal{A}$ be the unique fractional ${\mathfrak O}_N$-ideal with…

The main object of this paper is the minus class groups associated to CM-fields as Galois modules. In a previous article of the authors, we introduced a notion of equivalence for modules and determined the equivalence classes of the minus…

We study the Iwasawa theory of the fine Selmer group associated to certain Galois representations. The vanishing of the $\mu$-invariant is shown to follow in some cases from a natural property satisfied by Galois deformation rings. We…

We give degree lower bounds for quotient line bundles of the lowest piece of a Hodge module induced by a complex variation of Hodge structures outside a simple normal crossing divisor, beyond the unipotent variation case. This note aims to…

For a prime number p, we denote by K the cyclotomic Z_p-extension of a number field k. For a finite set S of prime numbers, we consider the S-ramified Iwasawa module which is the Galois group of the maximal abelian pro-p-extension of K…

We discuss Euler characteristics for finitely generated modules over Iwasawa algebras. We show that the Euler characteristic of a module is well-defined whenever the 0th homology group is finite if and only if the relevant compact p-adic…

A theorem of Grothendieck tells us that if the Galois action on the Tate module of an abelian variety factors through a smaller field, then the abelian variety, up to isogeny and finite extension of the base, is itself defined over the…

We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group. For any linear algebraic group G given as a semidirect product of a finite subgroup and a normal subgroup that is a…

In this paper we introduce and study the concept of cyclic subgroup commutativity degree of a finite group $G$. This quantity measures the probability of two random cyclic subgroups of $G$ commuting. Explicit formulas are obtained for some…

In this paper, we study the module-theoretic structure of classical Iwasawa modules. More precisely, for a finite abelian $p$-extension $K/k$ of totally real fields and the cyclotomic $\mathbb{Z}_p$-extension $K_{\infty}/K$, we consider…

Deconstructibility is an often-used sufficient condition on a class $\mathcal{C}$ of modules that allows one to carry out homological algebra \emph{relative to $\mathcal{C}$}. The principle \textbf{Maximum Deconstructibility (MD)} asserts…

At finite $N$ the ring of gauge invariant operators is not freely generated. For problems of interest in physics, these rings are Cohen--Macaulay and admit a Hironaka decomposition, in which the full invariant ring is a free module over a…

In this paper, we prove an existence theorem of a local moduli space for geometric structures in a very general setting. Then to show the interest of this result, we apply it to the case of sasakian and Sasaki-Einstein structures.

For sigma-PWB extensions, we extend to modules the theory of Gr\"obner bases of left ideals presented in [5]. As an application, if A is a bijective quasi-commutative sigma-PWB extension, we compute the module of syzygies of a submodule of…

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying…