A Gersten–Witt spectral sequence for regular schemes

Paul Balmer; Charles Walter

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Let $n$ be a positive integer and $A^{'}$ a complete characteristic zero discrete valuation ring with maximal ideal $𝔪$ , absolute ramification index $e < p - 1$ and perfect residue field $k$ of characteristic $p > 2$ . In this paper we classify smooth finite dimensional formal $p$ - groups over $A_{n}^{'} = A^{'} / 𝔪^{n} A^{'}$ , groups on which the “multiplication by $p$ ” morphism is faithfully flat, in particular $p$ -divisible groups. As applications, we prove that $p$ -divisible groups over $k$ , and the morphisms between them, lift canonically to $A^{'} / p A^{'}$ , and...