Relative Bogomolov extensions

Robert Grizzard

Displaying similar documents to “Relative Bogomolov extensions”

Normal integral bases and tameness conditions for Kummer extensions

Ilaria Del Corso, Lorenzo Paolo Rossi (2013)

Acta Arithmetica

Similarity:

We present a detailed analysis of some properties of a general tamely ramified Kummer extension of number fields L/K. Our main achievement is a criterion for the existence of a normal integral basis for a general Kummer extension, which generalizes the existing results. Our approach also allows us to explicitly describe the Steinitz class of L/K and we get an easy criterion for this class to be trivial. In the second part of the paper we restrict to the particular case of tame Kummer...

Greenberg’s conjecture for $ℤ_{p}^{d}$ -extensions

Andrea Bandini (2003)

Acta Arithmetica

Similarity:

Ergodicity of ℤ² extensions of irrational rotations

Yuqing Zhang (2011)

Studia Mathematica

Similarity:

Let = [0,1) be the additive group of real numbers modulo 1, α ∈ be an irrational number and t ∈ . We study ergodicity of skew product extensions T : × ℤ² → × ℤ², $T (x, s ₁, s ₂) = (x + α, s ₁ + 2 χ_{[0, 1 / 2)} (x) - 1, s ₂ + 2 χ_{[0, 1 / 2)} (x + t) - 1)$ .

Class group of a cyclotomic $ℤ_{p} \times ℤ_{ℓ}$ -extension

Humio Ichimura (2011)

Acta Arithmetica

Similarity:

The power set of ω Elementary submodels and weakenings of CH

István Juhász, Kenneth Kunen (2001)

Fundamenta Mathematicae

Similarity:

We define a new principle, SEP, which is true in all Cohen extensions of models of CH, and explore the relationship between SEP and other such principles. SEP is implied by each of CH*, the weak Freeze-Nation property of (ω), and the (ℵ₁,ℵ₀)-ideal property. SEP implies the principle $C ₂^{s} (ω ₂)$ , but does not follow from $C ₂^{s} (ω ₂)$ , or even $C^{s} (ω ₂)$ .

The importance of rational extensions

Frans Loonstra (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

The rational completion $\bar{M}$ of an $R$ -module $M$ can be characterized as a $\tau_{M}$ -injective hull of $M$ with respect to a (hereditary) torsion functor $\tau_{M}$ depending on $M$ . Properties of a torsion functor depending on an $R$ -module $M$ are studied.

Preservation of properties of a map by forcing

Akira Iwasa (2022)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $f : X \to Y$ be a continuous map such as an open map, a closed map or a quotient map. We study under what circumstances $f$ remains an open, closed or quotient map in forcing extensions.

On the compositum of all degree $d$ extensions of a number field

Itamar Gal, Robert Grizzard (2014)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We study the compositum $k^{[d]}$ of all degree $d$ extensions of a number field $k$ in a fixed algebraic closure. We show $k^{[d]}$ contains all subextensions of degree less than $d$ if and only if $d \leq 4$ . We prove that for $d > 2$ there is no bound $c = c (d)$ on the degree of elements required to generate finite subextensions of $k^{[d]} / k$ . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of $d$ , but that one can take $c = d$ when $d$ is prime. This question was inspired by work of...

Piecewise hereditary algebras under field extensions

Jie Li (2021)

Czechoslovak Mathematical Journal

Similarity:

Let $A$ be a finite-dimensional $k$ -algebra and $K / k$ be a finite separable field extension. We prove that $A$ is derived equivalent to a hereditary algebra if and only if so is $A \otimes_{k} K$ .

The importance of rational extensions

Frans Loonstra (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

The torsion subgroup of a family of elliptic curves over the maximal abelian extension of $ℚ$

Jerome Tomagan Dimabayao (2020)

Czechoslovak Mathematical Journal

Similarity:

We determine explicitly the structure of the torsion group over the maximal abelian extension of $ℚ$ and over the maximal $p$ -cyclotomic extensions of $ℚ$ for the family of rational elliptic curves given by $y^{2} = x^{3} + B$ , where $B$ is an integer.

Generic extensions of models of ZFC

Lev Bukovský (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models $M \subseteq N$ of ZFC with same ordinals, the condition $A p r_{M, N} (κ)$ implies that $N$ is a $κ$ -C.C. generic extension of $M$ .

Arithmetic of 0-cycles on varieties defined over number fields

Yongqi Liang (2013)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let $X$ be a rationally connected algebraic variety, defined over a number field $k .$ We find a relation between the arithmetic of rational points on $X$ and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for $K$ -rational points on $X_{K}$ for all finite extensions $K / k;$ (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles...

Obstruction sets and extensions of groups

Francesca Balestrieri (2016)

Acta Arithmetica

Similarity:

Let X be a nice variety over a number field k. We characterise in pure “descent-type” terms some inequivalent obstruction sets refining the inclusion $X {(_{k})}^{é t, B r} \subset X {(_{k})}^{B r ₁}$ . In the first part, we apply ideas from the proof of $X {(_{k})}^{é t, B r} = X {(_{k})}^{_{k}}$ by Skorobogatov and Demarche to new cases, by proving a comparison theorem for obstruction sets. In the second part, we show that if $\subset \subset_{k}$ are such that $\subset E x t (,_{k})$ , then $X {(_{k})}^{} = X {(_{k})}^{}$ . This allows us to conclude, among other things, that $X {(_{k})}^{é t, B r} = X {(_{k})}^{_{k}}$ and $X {(_{k})}^{S o l, B r ₁} = X {(_{k})}^{S o l_{k}}$ .

A characterization of Eisenstein polynomials generating extensions of degree $p^{2}$ and cyclic of degree $p^{3}$ over an unramified $𝔭$ -adic field

Maurizio Monge (2014)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $p \neq 2$ be a prime. We derive a technique based on local class field theory and on the expansions of certain resultants allowing to recover very easily Lbekkouri’s characterization of Eisenstein polynomials generating cyclic wild extensions of degree $p^{2}$ over $ℚ_{p}$ , and extend it to when the base fields $K$ is an unramified extension of $ℚ_{p}$ . When a polynomial satisfies a subset of such conditions the first unsatisfied condition characterizes the Galois group of the normal closure. We...

Troesch complexes and extensions of strict polynomial functors

Antoine Touzé (2012)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We develop a new approach of extension calculus in the category of strict polynomial functors, based on Troesch complexes. We obtain new short elementary proofs of numerous classical $Ext$ -computations as well as new results. In particular, we get a cohomological version of the “fundamental theorems” from classical invariant theory for $G L_{n}$ for $n$ big enough (and we give a conjecture for smaller values of $n$ ). We also study the “twisting spectral sequence” $E^{s, t} (F, G, r)$ converging to the extension groups...