Explicit construction of killed by $p$ finite flat group schemes over a $p$-adic complete discrete valuation ring

Finite commutative flat $p$-group schemes over a $p$-adic cdv ring were described during last decade (C.Breuil, M.Kisin) under the traditional restriction $p>2$. Recently (E.Lau, W.Kim) considered the case $p=2$. All above results were deduced from the corresponding classification of $p$-divisible groups. On the other hand the author gave several years ago a direct approach to Breuil's classification for group schemes killed by $p>2$ and recently extended this result to the case $p=2$. Basic ideas of this approach will be explained at the talk.