11 citations · 79 across the 19 of their papers we have counts for
19 papers
A heuristic for ray class groups of quadratic number fields
Alex Bartel, Carlo Pagano
We formulate a model for the average behaviour of ray class groups of real quadratic fields with respect to a fixed rational modulus, locally at a finite set of odd primes. To…
Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups
Alex Bartel, Adam Morgan
We address several seemingly disparate problems in arithmetic geometry: the statistical behaviour of the Galois module structure of Mordell--Weil groups of a fixed elliptic curve o…
Vignéras orbifolds: isospectrality, regulators, and torsion homology
Alex Bartel, Aurel Page
We develop a new approach to the isospectrality of the orbifolds constructed by Vignéras. We give fine sufficient criteria for i-isospectrality in given degree i and for representa…
Arakelov class groups of random number fields
Alex Bartel, Henri Johnston, Hendrik W. Lenstra
The main purpose of the paper is to formulate a probabilistic model for Arakelov class groups in families of number fields, offering a correction to the Cohen--Lenstra--Martinet he…
On class groups of random number fields
Alex Bartel, Hendrik W. Lenstra
The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in t…
Relations between permutation representations in positive characteristic
Alex Bartel, Matthew Spencer
Given a finite group G and a field F, a G-set X gives rise to an F[G]-permutation module F[X]. This defines a map from the Burnside ring of G to its representation ring over F. It…
Group representations in the homology of 3-manifolds
Alex Bartel, Aurel Page
If M is a manifold with an action of a group G, then the homology group H_1(M,Q) is naturally a Q[G]-module, where Q[G] denotes the rational group ring. We prove that for every fin…
A note on Green functors with inflation
Alex Bartel, Matthew Spencer
This note is motivated by the problem to understand, given a commutative ring F, which G-sets X, Y give rise to isomorphic F[G]-representations F[X]\cong F[Y]. A typical step in su…
Torsion homology and regulators of isospectral manifolds
Alex Bartel, Aurel Page
Given a finite group G, a G-covering of closed Riemannian manifolds, and a so-called G-relation, a construction of Sunada produces a pair of manifolds M_1 and M_2 that are strongly…
Commensurability of automorphism groups
Alex Bartel, Hendrik W. Lenstra
We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are…
Rational representations and permutation representations of finite groups
Alex Bartel, Tim Dokchitser
We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is kno…
Simplicity of twists of abelian varieties
Alex Bartel
We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.
Factor equivalence of Galois modules and regulator constants
Alex Bartel
We compare two approaches to the study of Galois module structures: on the one hand factor equivalence, a technique that has been used by Fröhlich and others to investigate the Gal…
Elliptic curves with p-Selmer growth for all p
Alex Bartel
It is known, that for every elliptic curve over Q there exists a quadratic extension in which the rank does not go up. For a large class of elliptic curves, the same is known with…
Brauer relations in finite groups II - quasi-elementary groups of order p^aq
Alex Bartel, Tim Dokchitser
This is the second in a series of papers investigating the space of Brauer relations of a finite group, the kernel of the natural map from its Burnside ring to the rational represe…
Index formulae for integral Galois modules
Alex Bartel, Bart de Smit
We prove very general index formulae for integral Galois modules, specifically for units in rings of integers of number fields, for higher K-groups of rings of integers, and for Mo…
Brauer relations in finite groups
Alex Bartel, Tim Dokchitser
If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to…
On Brauer-Kuroda type relations of S-class numbers in dihedral extensions
Alex Bartel
Let F/k be a Galois extension of number fields with dihedral Galois group of order 2q, where q is an odd integer. We express a certain quotient of S-class numbers of intermediate f…
Large Selmer groups over number fields
Alex Bartel
Let p be a prime number and M a quadratic number field, M not equal to Q(\sqrt{p}) if p is congruent to 1 modulo 4. We will prove that for any positive integer d there exists a Gal…