The modern geometric treatment now refers to some basic papers of David Mumford, from 1966 to 1967, which reformulated that theory in terms from abstract algebraic geometry valid over general fields.
Computer algebra techniques are now able to have some impact on the direct handling of equations for small values of d > 1.
There is a uniqueness result for irreducible linear representations of the theta group with given central character, or in other words an analogue of the Stone–von Neumann theorem.
The goal of the theory is to prove results on the homogeneous coordinate ring of the embedded abelian variety A, that is, set in a projective space according to a very ample L and its global sections.
For a base field of characteristic zero, Giuseppe Pareschi proved a result including these (as the cases p = 0, 1) which had been conjectured by Lazarsfeld: let L be an ample line bundle on an abelian variety A.