Abelian surfaces over finite fields containing no curves of genus $3$ or
less
Abelian surfaces over finite fields containing no curves of genus $3$ or
less
We characterise abelian surfaces defined over finite fields containing no curves of genus less than or equal to $3$. Firstly, we complete and expand the characterisation of isogeny classes of abelian surfaces with no curves of genus up to $2$ initiated by the first author et al. in previous work. …