Cm Seminar Talk Notes

We define two such pairs (X, i), (Y, j) to be equivalent if there is an isogeny α : X → Y such that if α̃ : End(X) ' End(Y ) is the induced isomorphism, we have α̃ ◦ i = j. It is easy to check that this is an equivalence relation. We write X ∼ Y if (X, i) is equivalent to (Y, j). Let AF be the collection of equivalence classes. We will classify such equivalence classes. Let D be any R-algebra. A C-algebra structure Φ on M is an R-algebra homomorphism Φ : C → D, so D can be seen as a C-algebra via Φ. We write DΦ to denote this C-algebra.