Rachel Newton

activity

20102026

most citedTranscendental Brauer groups of products of CM elliptic curves

15 citations · 49 across the 19 of their papers we have counts for

collaborators

22 papers

math.NT2026

The Hasse norm principle for $A_{4}$ -quartic extensions of global function fields

Anand Deopurkar, Rachel Newton, Vaidehee Thatte +1

For a finite extension of global fields $K / k$ , the norm map $N_{K / k} : K^{\times} \to k^{\times}$ extends to a map on idèle groups. The Hasse norm principle holds if every element of $…

math.AG2026

Refined obstructions to local-global principles for 0-cycles

Francesca Balestrieri, Anouk Greven, Rachel Newton +3

We introduce new `refined' obstructions to local-global principles for 0-cycles on algebraic varieties over number fields. Assuming finiteness of relevant Tate--Shafarevich groups,…

math.NT2023

The Hasse norm principle for abelian extensions -- corrigendum

Christopher Frei, Daniel Loughran, Rachel Newton

The proofs of Theorem 1.1 and Theorem 1.5(2) in the authors' paper 'The Hasse norm principle for abelian extensions' are incorrect. We point out the mistakes and provide correct pr…

math.NT2022

Distribution of genus numbers of abelian number fields

Christopher Frei, Daniel Loughran, Rachel Newton

We study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the gen…

math.AG2020★ 3 cited

Evaluating the wild Brauer group

Martin Bright, Rachel Newton

Classifying elements of the Brauer group of a variety X over a p-adic field according to the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filt…

math.NT2020

The Hasse Norm Principle in Global Function Fields

Adelina Mânzăţeanu, Rachel Newton, Ekin Ozman +2

Let $L$ be a finite extension of $F_{q} (t)$ . We calculate the proportion of polynomials of degree $d$ in $F_{q} [t]$ that are everywhere locally norms from $L/\mathbb{…

math.NT2019★ 2 cited

Explicit methods for the Hasse norm principle and applications to $A_{n}$ and $S_{n}$ extensions

André Macedo, Rachel Newton

Let $K / k$ be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for $K / k$ and the…

math.NT2018★ 5 cited

Number fields with prescribed norms

Christopher Frei, Daniel Loughran, Rachel Newton +2

We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$ , from which a given finite set of elements of $k$ are norms. In particular, we sho…

math.NT2018★ 6 cited

Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces

Francesca Balestrieri, Rachel Newton

Let $k$ be a number field. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational points over finite extensions of $k$ to that of zero-cycles over $k$ for…

math.NT2018

Arithmetic of rational points and zero-cycles on Kummer varieties

Francesca Balestrieri, Rachel Newton

Let $k$ be a number field, let $X$ be a Kummer variety over $k$ , and let $δ$ be an odd integer. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational poin…

math.NT2017

Non-ordinary curves with a Prym variety of low $p$ -rank

Turku Ozlum Celik, Yara Elias, Burcin Gunes +4

If $π : Y \to X$ is an unramified double cover of a smooth curve of genus $g$ , then the Prym variety $P_{π}$ is a principally polarized abelian variety of dimension $g - 1$ . When $X$ is…

math.NT2016

Shadow lines in the arithmetic of elliptic curves

Jennifer S. Balakrishnan, Mirela Ciperiani, Jaclyn Lang +2

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a correspond…

math.NT2016

A bound on the primes of bad reduction for CM curves of genus 3

Pınar Kılıçer, Kristin Lauter, Elisa Lorenzo García +3

We give bounds on the primes of geometric bad reduction for curves of genus three of primitive CM type in terms of the CM orders. In the case of genus one, there are no primes of g…

math.QA2016★ 4 cited

Orbifold autoequivalent exceptional unimodal singularities

Ana Ros Camacho, Rachel Newton

We prove that different expressions of the same exceptional unimodal singularity are orbifold equivalent. As in our previous paper, the matrix factorizations proving these orbifold…

math.GT2016

Counting curve types

Tarik Aougab, Juan Souto

Let $S$ be a closed orientable hyperbolic surface, and let $O (K, S)$ denote the number of mapping class group orbits of curves on $S$ with at most $K$ self-intersections.…

math.QA2015★ 11 cited

Strangely dual orbifold equivalence I

Rachel Newton, Ana Ros Camacho

In this brief note we prove orbifold equivalence between two potentials described by strangely dual exceptional unimodular singularities of type $K_{14}$ and $Q_{10}$ in two differ…

math.NT2015★ 3 cited

The Hasse norm principle for abelian extensions

Christopher Frei, Daniel Loughran, Rachel Newton

We study the distribution of abelian extensions of bounded discriminant of a number field $k$ which fail the Hasse norm principle. For example, we classify those finite abelian gro…

math.NT2015★ 15 cited

Transcendental Brauer groups of products of CM elliptic curves

Rachel Newton

Let $L$ be a number field and let $E / L$ be an elliptic curve with complex multiplication by the ring of integers $O_{K}$ of an imaginary quadratic field $K$ . We use class f…

math.NT2014

Bad reduction of genus $3$ curves with complex multiplication

Irene Bouw, Jenny Cooley, Kristin Lauter +4

Let $C$ be a smooth, absolutely irreducible genus- $3$ curve over a number field $M$ . Suppose that the Jacobian of $C$ has complex multiplication by a sextic CM-field $K$ . Suppose f…

math.NT2013

Realising the cup-product of local Tate duality

Rachel Newton

We present an explicit description, in terms of central simple algebras, of a cup-product map which occurs in the statement of local Tate duality for Galois modules of prime order…

math.NT2013

Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve

Tom Fisher, Rachel Newton

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modific…

math.NT2010

Explicit local reciprocity for tame extensions

Rachel Newton

We consider a tamely ramified abelian extension of local fields of degree n, without assuming the presence of the nth roots of unity in the base field. We give an explicit formula…

The Hasse norm principle for A4​-quartic extensions of global function fields

Refined obstructions to local-global principles for 0-cycles

The Hasse norm principle for abelian extensions -- corrigendum

Distribution of genus numbers of abelian number fields

Evaluating the wild Brauer group

The Hasse Norm Principle in Global Function Fields

Explicit methods for the Hasse norm principle and applications to An​ and Sn​ extensions

Number fields with prescribed norms

Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces

Arithmetic of rational points and zero-cycles on Kummer varieties

Non-ordinary curves with a Prym variety of low p-rank

Shadow lines in the arithmetic of elliptic curves

A bound on the primes of bad reduction for CM curves of genus 3

Orbifold autoequivalent exceptional unimodal singularities

Counting curve types

Strangely dual orbifold equivalence I

The Hasse norm principle for abelian extensions

Transcendental Brauer groups of products of CM elliptic curves

Bad reduction of genus 3 curves with complex multiplication

Realising the cup-product of local Tate duality

Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve

Explicit local reciprocity for tame extensions

The Hasse norm principle for $A_{4}$ -quartic extensions of global function fields

Explicit methods for the Hasse norm principle and applications to $A_{n}$ and $S_{n}$ extensions

Non-ordinary curves with a Prym variety of low $p$ -rank

Bad reduction of genus $3$ curves with complex multiplication