Related papers: Fitting ideals of class groups for CM abelian exte…

In a previous paper we constructed a new class of Iwasawa modules as $\ell$--adic realizations of what we called abstract $\ell$--adic $1$--motives in the number field setting. We proved in loc. cit. that the new Iwasawa modules satisfy an…

We study the capitulation of ideal classes in an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $k =Q(\sqrt{2pq}, i)$, where $i=\sqrt{-1}$ and $p\equiv -q\equiv1 \pmod 4$ are different primes. For each…

The aim of this paper is to study some distinguished classes of $k$-ideals of semirings, which include $k$-prime, $k$-semiprime, $k$-radical, $k$-irreducible, and $k$-strongly irreducible ideals. We discuss some of the properties of…

A classical theorem due to Mycielski states that an equivalence relation $E$ having the Baire property and meager equivalence classes must have a perfect set of pairwise inequivalent elements. We consider equivalence relations with…

We study the Fitting ideals over the finite layers of the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ of Selmer groups attached to the Rankin--Selberg convolution of two modular forms $f$ and $g$. Inspired by the Theta elements for…

We describe an explicit `higher rank' Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of general number fields. We then show that this theory leads to a concrete new strategy for proving…

In this article, we study combinatorial properties of a certain ideal on $\omega$, called the \emph{Splitting ideal}. We calculate its cardinal invariants and its position in the Kat\v{e}tov order among other definable ideals. We also study…

We describe a general framework for prime, completely prime, semiprime, and primitive ideals of an abelian 2-category. This provides a noncommutative version of Balmer's prime spectrum of a tensor triangulated category. These notions are…

T. De Medts, Y. Segev and K. Tent [Special Moufang sets, their root groups and their \mu-maps, Proc. Lond. Math. Soc. (3) 96 (2008), 767-791] proved that the little projective group of a special Moufang set M(U,\tau) is perfect provided…

In this paper, we study some new examples of ideals on $\omega$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order -- known as the…

Let p be an odd prime. Let F_p^* be the no-null part of the finite field of p elements. Let K=\Q(zeta) be a p-cyclotomic field and O_K be its ring of integers. Let pi be the prime ideal of K lying over p. Let sigma : zeta --> zeta^v be the…

We correct the faulty formulas given in a previous article and we compute the defect group for the Iwasawa $\lambda$ invariants attached to the S-ramified T-decomposed a belian pro-${\ell}$-extensions on the Z${\ell}$-cyclotomic extensionof…

Inspired by results for graph $C^*$-algebras, we investigate connections between the ideal structure of an inverse semigroup $S$ and that of its tight $C^*$-algebra by relating ideals in $S$ to certain open invariant sets in the associated…

Let $k$ be a fixed finite geometric extension of the rational function field $\mathbb{F}_q(t)$. Let $F/k$ be a finite abelian extension such that there is an $\Fq$-rational place $\infty$ in $k$ which splits in $F/k$ and let $\mathcal{O}_F$…

We observe that any regular Lie groupoid G over an manifold M fits into an extension $K \to G \to E$ of a foliation groupoid E by a bundle of connected Lie groups K. If $\FF$ is the foliation on M given by the orbits of E and T is a…

Let T be a complete local ring and C a finite set of incomparable prime ideals of T. We find necessary and sufficient conditions for T to be the completion of an integral domain whose generic formal fiber is semilocal with maximal ideals…

Let $q$ be a non-negative integer. We prove that a perfect field $K$ has cohomological dimension at most $q+1$ if, and only if, for any finite extension $L$ of $K$ and for any homogeneous space $Z$ under a smooth linear connected algebraic…

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…

In this paper, we present a unifying approach to the general theory of abelian Stark conjectures. To do so we define natural notions of `zeta element', of `Weil-\'etale cohomology complexes' and of `integral Selmer groups' for the…

For an elliptic curve $E$ over $\mathbb{Q}$, putting $K=\mathbb{Q}(E[p])$ which is the $p$-th division field of $E$ for an odd prime $p$, we study the ideal class group $\mathrm{Cl}_K$ of $K$ as a $\mathrm{Gal}(K/\mathbb{Q})$-module. More…