11 citations · 79 across the 19 of their papers we have counts for
11 papers · 1 filter
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…
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…
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…
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…