Let A be an abelian variety over a number field, with a good reduction at a prime ideal containing a prime number p. Denote A as an abelian variety over a finite field of characteristic p, which is obtained by the reduction of A at the prime ideal. In this study, we derive an algorithm that allows us to decompose the group scheme A[p] into indecomposable quasi-polarized BT1-group schemes up to isomorphism. This can be achieved for the unramified p based on its decomposition into prime ideals in the endomorphism algebra of A. We also compute all types of these correspondences for abelian varieties with dimensions up to 5. As a consequence, we establish the relationship between the decompositions of prime p and the corresponding pairs of p-rank and a-number for an abelian variety A.
- Abelian varieties
- Group schemes