Honda systems of group schemes of period $p$

A direct construction is given of the Fontaine anti-equivalence between the subcategories of finite commutative group schemes over the ring of Witt vectors and of finite Honda systems in the case of objects annihilated by multiplication by $p$ (for $p=2$ there is no restriction involving the unipotency of the corresponding objects). An explicit description of the algebras of group schemes of the category under consideration is obtained and it is shown that the bifunctor $\operatorname{Ext}^2$ in this category is identically equal to zero.
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