Wojciech J. Gajda

In joint work Francesco Campagna, we classify all such abelian varieties. The main difficulty in doing so is due to the existence of a simple group scheme V of order 4 which is everywhere locally reducible (but globally irreducible). This makes it hard to classify extensions of V by itself. A key step in being able to do so comes from proving the failure of a type of local-global principle for finite flat group schemes. In this talk I will give an introduction to finite flat group schemes and outline a proof of the above.