9 papers
Selfless nonnuclear crossed products
Jamie Bell
For a strictly ergodic action of a countable discrete group with Ozawa's property PHP on the Cantor set, we prove that dynamical comparison implies complete selflessness of its red…
Factorisation and matrix amplification of real rank zero inclusions
Jamie Bell
We show that real rank zero is not preserved under matrix amplifications of inclusions. This yields real rank zero inclusions that do not approximately factor through real rank zer…
Nonamenable groups whose reduced group C*-algebras are not pure
Jamie Bell
We exhibit nonamenable groups whose reduced group C*-algebras are not pure. More precisely, if is any countably infinite discrete group, then the reduced group C*-algebra of th…
Nonnuclear Bunce-Deddens algebras
Jamie Bell
We introduce nonnuclear Bunce-Deddens algebras, defined as reduced crossed product C*-algebras associated with free odometer actions of nonamenable countable discrete residually fi…
Crossed product C*-algebras associated with non-minimal actions on the circle
Jamie Bell
We examine crossed product C*-algebras associated with free non-minimal actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt,…
Stable rank one in nonnuclear crossed products
Jamie Bell, Shirly Geffen, David Kerr
We initiate an investigation into the local structure of simple nonnuclear C-crossed products by showing that stable rank one is generic within two natural classes of minimal a…
Non-Isomorphic Abelian Varieties with the Same Arithmetic
Jamie Bell
We construct two abelian varieties over which are not isomorphic, but have isomorphic Mordell--Weil groups over every number field, isomorphic Tate modules and equal v…
A Note on the Growth of Sha in Dihedral Extensions
Jamie Bell
We provide a formula for the order of the Tate--Shafarevich group of elliptic curves over dihedral extensions of number fields of order , up to powers and primes divid…
p-Selmer ranks of CM abelian varieties
Jamie Bell
For an elliptic curve with complex multiplication over a number field, the --Selmer rank is even for all . Česnavičius proved this using the fact that admits a $…