The 2-torsion field of an abelian variety is the minimal field extension over which the 2-torsion subgroup of its Mordell-Weil group is rational; it is a Galois extension of the field over which the abelian variety is defined.
For abelian varieties over number fields, the 2-torsion field is specified by giving a number field of minimal degree and absolute discriminant whose Galois closure is equal to the 2-torsion field.
- Review status: reviewed
- Last edited by Andrew Sutherland on 2018-06-08 05:30:07
- 2018-06-08 05:30:07 by Andrew Sutherland (Reviewed)