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Finite group schemes over bases with low ramification. (English) Zbl 0984.14015

Let \(A\) be a complete characteristic \((0,p)\) discrete valuation ring with absolute ramification degree \(e\) and a perfect residue field. When \(e=1\), Fontaine constructed an anti-equivalence between the category of finite and flat commutative group schemes over \(A\) and the category of finite Honda systems over \(A\).
In this paper, the author generalizes Fontaine’s result to the case \(e\) less than or equal to \(p-1\). This paper lays the foundations for generalizing Ramakrishna’s work on deformations of Galois representations.

MSC:

14L15 Group schemes
14L05 Formal groups, \(p\)-divisible groups
13F30 Valuation rings
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