Related papers: On Cebotarev sets

Chebotarev's density theorem asserts that the prime ideals are equidistributed among the conjugacy classes of the Galois group of any normal extension of number fields. An effective version of this theorem was first established by Lagarias…

We show how topology of a space may lead to tensor fields on (the smooth part of) moduli spaces of the fundamental group.

The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria…

This paper builds fundamental perfect fields of positive characteristic and shows the structure of perfect fields that a field of positive characteristic is a perfect field if and only if it is an algebraic extension of a fundamental…

We introduce a pro-cdh topology on formal schemes and prove that the $\infty$-topos of pro-cdh sheaves of spaces has an optimal bound of homotopy dimension. This remedies a defect for a pro-cdh topology on schemes introduced in [KS23]. As…

Let $K\geq 2$ be a natural number and $a_i,b_i\in\mathbb{Z}$ for $i=1,\ldots,K-1$. We use the large sieve to derive explicit upper bounds for the number of prime $k$-tuplets, i.e., for the number of primes $p\leq x$ for which all $a_ip+b_i$…

We give a brief review of the application of some topological solutions in field theory.

We introduce the concept of linear topological modules over vertex algebras and apply it to representations of $\beta-\gamma$ system and affine Kac-Moody algebras.

In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…

In this paper we have introduced the notion of $\mathcal{I}$-sparse set in the space of reals and explored some properties of the family of $\mathcal{I}$-sparse sets. Thereafter we have induced a topology namely $\mathcal{I}$-sparse set…

A criterion for determining exactly when an order of a maximal subfield of a central simple algebra over a number field can be embedded into an order of this algebra is given. Various previous results have been generalized and recovered by…

In this paper we discuss the notion of completeness of topologized posets and survey some recent results on closedness properties of complete topologized semilattices.

We investigate generalizations of the topology of the higher Cantor space on $2^\kappa$, based on arbitrary ideals rather than the bounded ideal on $\kappa$. Our main focus is on the topology induced by the nonstationary ideal, and we call…

A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove a new Cartan-type property for the fine topology in the case $p=1$. Then we use this property to prove the existence of…

We present the set of axioms for topological space with the operation of boundary as primitive notion.

Berge's maximum theorem gives conditions ensuring the continuity of an optimised function as a parameter changes. In this paper we state and prove the maximum theorem in terms of the theory of monoidal topology and the theory of double…

We describe first-degree prime ideals of biquadratic extensions in terms of first-degree prime ideals of two underlying quadratic fields. The identification of the prime divisors is given by numerical conditions involving their ideal norms.…

This article investigates various notions of primeness for one-sided ideals in noncommutative rings, with a focus on principal ideal domains.

Let $R$ be a regular ring of dimension $d$ containing a field $K$ of characteristic zero. If $E$ is an $R$-module let $Ass^i E = \{ Q \in \ Ass E \mid \ height Q = i \}$. Let $P$ be a prime ideal in $R$ of height $g$. We show that if $R/P$…