Related papers: Kolyvagin systems of Stark units

Colored planar rook algebra is a semigroup algebra in which the basis element has a diagrammatic description. The category of finite dimensional modules over this algebra is completely reducible and suitable functors are defined on this…

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…

There are familiar examples of computable structures having various computable Scott ranks. There are also familiar structures, such as the Harrison ordering, which have Scott rank $\omega_1^{CK}+1$. Makkai produced a structure of Scott…

Given an abelian, CM extension K of any totally real number field k, we consider two conjectures `of Stark type'. The `Integrality Conjecture' concerns the image of a p-adic map `\mathfrak{s}_{K/k,S}' determined by the minus-part of the…

As remarked in [Kolyvagin systems, by Barry Mazur and Karl Rubin] Proposition 6.2.6 and Buyukboduk[ arXiv:0706.0377v1 ] Remark 3.25 one does not expect the Kolyvagin system obtained from an Euler system for a p-adic Galois representation T…

We prove a noncommutative variant of Saskin's classical theorem -- on the connection between Choquet boundaries for function spaces and Korovkin sets -- for operator systems generating separable Type I C*-algebras. The main result implies…

The principal goal of this paper is to develop Kolyvagin's descent to apply with the big Heegner point Euler system constructed by Howard for the big Galois representation $\mathbb{T}$ attached to a Hida family $\mathbb{F}$ of elliptic…

We introduce Kurosh elements in division rings based on the idea of a conjecture of Kurosh. Using this, we generalize a result of Faith in [3] and of Herstein in [6].

We use sheaves and algebraic L-theory to construct the rational Pontryagin classes of fiber bundles with fiber R^n. This amounts to an alternative proof of Novikov's theorem on the topological invariance of the rational Pontryagin classes…

We find an explicit presentation of relative odd unitary Steinberg groups constructed by odd form rings and of relative doubly laced Steinberg groups over commutative rings, i.e. the Steinberg groups associated with the Chevalley group…

The classical work of Feferman Vaught gives a powerful, constructive analysis of definability in (generalized) product structures, and certain associated enriched Boolean structures. %structures in terms of definability in the component…

The conditions for stability of the elements of linear groups over the associative rings with identity and their connection with the stability of rings are analyzed in the article. The stability of rings which are commutative, satisfy the…

Let R be a ring and G a group. An R-module A is said to be artinian-by-(finite rank) if TorR(A) is artinian and A/TorR(A) has finite R-rank. The authors study ZG-modules A such that A/CA(H) is artinian-by-(finite rank) (as a Z-module) for…

Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga-Sato variety over a suitable Shimura curve which gives rise…

In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations…

Given an odd prime number $p$ and a $p$-stabilized Artin representation $\rho$ over $\mathbb{Q}$, we introduce a family of $p$-adic Stark regulators and we formulate an Iwasawa-Greenberg main conjecture and a $p$-adic Stark conjecture which…

L\'evai and Pyber proposed the following as a conjecture: Let $G$ be a profinite group such that the set of solutions of the equation $x^n=1$ has positive Haar measure. Then $G$ has an open subgroup $H$ and an element $t$ such that all…

A Kirkman triple system of order $v$, KTS$(v)$, is a resolvable Steiner triple system on $v$ elements. In this paper, we investigate an open problem posed by Doug Stinson, namely the existence of KTS$(v)$ which contain as a subdesign a…

Given a standard graded polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic zero and a graded $k$-subalgebra $A=k[f_1,...,f_m]\subset R$, one relates the module $\Omega_{A/k}$ of K\"ahler $k$-differentials of $A$ to the…

In this article, we first generalize Kaplansky's zero-divisor conjecture of group-rings $K[G]$ (with $K$ a field) to the more general setting of $G$-graded rings $R=\bigoplus\limits_{n\in G}R_{n}$ with $G$ a torsion-free group. Then we…