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

The Iwasawa manifold is uplifted to seven-folds of either G_2 holonomy or SU(3) structure, explicit new metrics for the same having been constructed in this work. We uplift the Iwasawa manifold to a G_2 manifold through "size" deformation…

Let $p$ be an odd prime number and $k$ an imaginary quadratic field in which $p$ splits. In this paper, we consider a weak form of Greenberg's generalized conjecture for $p$ and $k$, which states that the non-trivial Iwasawa module of the…

We prove a modularity lifting theorem for minimally ramified deformations of two-dimensional odd Galois representations, over an arbitrary number field. The main ingredient is a generalization of the Taylor-Wiles method in which we patch…

We give sufficient conditions on $p$-blocks of $p$-nilpotent groups over $\mathbb{F}_p$ to be splendidly Rickard equivalent and $p$-permutation equivalent to their Brauer correspondents. The paper also contains Galois descent results on…

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…

There is a constrained-WZNW--Toda theory for any simple Lie algebra equipped with an integral gradation. It is explained how the different approaches to these dynamical systems are related by gauge transformations. Combining Gauss…

We classify possible types of pseudomoduli which arise when supersymmetry is dynamically broken in infrared-free low-energy theories. We show that, even if the pseudomoduli potential is generated only at higher loops, there is a regime…

We study properties of ramification in Iwasawa modules.

Riemannian Einstein solvmanifolds can be described in terms of nilsolitons, namely nilpotent Lie groups endowed with a left-invariant Ricci soliton metric. This characterization does not extend to indefinite metrics; nonetheless,…

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. In a previous article, we gave a necessary and sufficient condition for X to be free of given rank d…

In this article, we introduce the concepts of graded $s$-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules,…

The general solution of the antifield-independent Wess-Zumino consistency condition is worked out for models involving exterior form gauge fields of arbitrary degree. We consider both the free theory and theories with Chapline-Manton…

Most of the examples of wavelet sets are for dilation sets which are groups. We find a necessary and sufficient condition under which subspace wavelet sets exist for dilation sets of the form $A B$, which are not necessarily groups. We…

Consider a reflection from a finitely-complete category $\mathbb{C}$ into its full subcategory $\mathbb{M}$, with unit $\eta :1_\mathbb{C}\rightarrow HI$. Suppose there is a left-exact functor $U$ into the category of sets, such that $UH$…

The equivariant `main conjecture' of Iwasawa theory is shown to hold for a Galois extension $K/k$ of number fields with Galois group an $l$-adic pro-$l$ Lie group of dimension 1 containing an abelian subgroup of index $l$, provided that…

In this paper, we construct, investigate and, in some cases, classify several new classes of (simple) modules over the Takiff $\mathfrak{sl}_{2}$. More precisely, we first explicitly construct and classify, up to isomorphism, all modules…

In this paper we investigate the unbounded Kasparov product between a differentiable module and an unbounded cycle of a very general kind that includes all unbounded Kasparov modules and hence also all spectral triples. Our assumptions on…

We consider a set of necessary conditions which are efficient heuristics for deciding when a set of Wang tiles cannot tile a group. Piantadosi gave a necessary and sufficient condition for the existence of a valid tiling of any free group.…

For a number field $F$ and an odd prime number $p,$ let $\tilde{F}$ be the compositum of all $\mathbb{Z}_p$-extensions of $F$ and $\tilde{\Lambda}$ the associated Iwasawa algebra. Let $G_{S}(\tilde{F})$ be the Galois group over $\tilde{F}$…

Let the finite group $G$ act linearly on the vector space $V$ over the field $k$ of arbitrary characteristic. If $H<G$ is a subgroup the extension of invariant rings $k[V]^G\subset k[V]^H$ is studied using modules of covariants. An example…