Research in Number Theory

Provando e riprovando (motto of Il Nuovo Cimento).

Antonella Perucca's research areas are Number Theory and Algebraic Geometry because she studies algebraic groups defined over number fields.
She is one of the leading experts in Kummer theory (from a review: Kummer extensions of number fields, a topic of significant classical interest and enduringly broad appeal in number theory). In the past, she focused on local-global principles (understanding how the properties of algebraic groups and their points can be detected from their reductions). Recently, she got interested in Artin's Conjecture on primitive roots.

Research group

Current members

Previous members


Bryan Advocaat, Alexandre Benoist, Peter Bruin, Chi Wa (Clifford) Chan, Christophe Debry, Jeroen Demeyer, Francesc Fité, Chris Hall, Fritz Hörmann, Olli Järviniemi, Tom Kasel, Peter Jossen, Davide Lombardo, Pieter Moree, Antigona Pajaziti, Flavio Perissinotto, Tim Seuré, Igor Shparlinski, Pietro Sgobba, Mia Tholl, Sebastiano Tronto, Vincent Wolff.


Reductions of points on algebraic groups

Detecting linear dependence and the support problem

Kummer theory (for number fields)

Artin's conjecture on primitive roots

Further topics