Alex Bartel
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View article: Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups
Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups Open
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 over varying quadratic extensions; the frequency of failure …
View article: Vignéras orbifolds: isospectrality, regulators, and torsion homology
Vignéras orbifolds: isospectrality, regulators, and torsion homology Open
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 representation equivalence. These allow us to produce very small exot…
View article: Arakelov class groups of random number fields
Arakelov class groups of random number fields Open
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 heuristic on ideal class groups. To that end, we show that Chin…
View article: PRM volume 152 issue 1 Cover and Front matter
PRM volume 152 issue 1 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
View article: PRM volume 151 issue 1 Cover and Front matter
PRM volume 151 issue 1 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
View article: Arakelov class groups of random number fields
Arakelov class groups of random number fields Open
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 heuristic on ideal class groups. To that end, we show that Ch…
View article: Galois module structure of oriented Arakelov class groups
Galois module structure of oriented Arakelov class groups Open
We show that Chinburg's Omega(3) conjecture implies tight restrictions on the Galois module structure of oriented Arakelov class groups of number fields. We apply our findings to formulating a probabilistic model for Arakelov class groups …
View article: Group representations in the homology of 3-manifolds
Group representations in the homology of 3-manifolds Open
If M is a manifold with an action of a group G , then the homology group H_1(M,\mathbb Q) is naturally a \mathbb Q[G] -module, where \mathbb Q[G] denotes the rational group ring. We prove that for every finite group G , and for every \math…
View article: Commensurability of automorphism groups
Commensurability of automorphism groups Open
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 infinite. This work is motivated by the Cohen–Lenstra heur…
View article: Torsion homology and regulators of isospectral manifolds
Torsion homology and regulators of isospectral manifolds Open
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 isospectral. Such manifolds have the same dimension and th…