6 papers
Integral Brauer--Manin Obstruction for Fermat Near Misses
Jessica Alessandrì, Jiazhi He
We study the integral Hasse principle for the affine surfaces given by , where is odd and squarefree. We give a criterion to determine if there is an integra…
Torsion points on -type abelian varieties
Jessica Alessandrì, Nirvana Coppola
It is well known that the order of the torsion group of an abelian variety over a number field divides the greatest common divisor of the sizes of points on the reduction at each p…
Fermat near misses and the integral Hilbert Property
Jessica Alessandrì, Daniel Loughran
We consider the Diophantine equation for , which is related to near misses for the quartic case of Fermat's Last Theorem. For certain we…
On the Hasse principle for divisibility in elliptic curves
Jessica Alessandrì, Laura Paladino
Let be a prime number and a positive integer. Let be an elliptic curve defined over a number field . It is known that the local-global divisibility by holds in $…
Local-global divisibility on algebraic tori
Jessica Alessandrì, Rocco Chirivì, Laura Paladino
We give a complete answer to the local-global divisibility problem for algebraic tori. In particular, we prove that given an odd prime , if is an algebraic torus of dimensio…
On 7-division fields of CM elliptic curves
Jessica Alessandrì, Laura Paladino
Let be a CM elliptic curve defined over a number field , with Weiestrass form or . For every positive integer , we denote by ${\mathcal{…