Jessica Alessandrì

The torsion subgroups of elliptic curves over the rational field are well known and classified thanks to Mazur's Theorem. In higher dimensional abelian varieties, however, a bound for the possible size of the rational torsion is not know. Even for abelian surfaces, a complete list of possible torsion subgroups is only known under some assumption on the endomorphism algebra (i.e. having potential quaternionic multiplication). In this talk, I will focus on GL_2-type abelian varieties: I will give a generalisation of a theorem of Katz that can be used to find an upper bound to and, sometimes, completely determine the size of the torsion subgroup. I will then show how to implement this result to produce a list of possible torsion subgroup orders for GL_2 abelian varieties over Q of a given dimension.  This is joint work with Nirvana Coppola (University of Padova).