Computing "isogeny graphs" using CM lattices
We describe a method to compute isogenies between polarized CM lattices.
Using this we can compute the graph structure of (l,l)-isogeny graphs of
abelian surfaces over finite fields. We stress the words "graph structure"
here, for we cannot determine absolute invariants of these objects in
characteristic p (in characteristic 0 we can find complex value approximations).
One positive aspect of this approach though is that computing endomorphism
rings requires very little effort. Some generalizations will be discussed
and some examples provided.