Relative crystalline representations and p-divisible groups in the small ramification case

Abstract

Let k be a perfect field of characteristic p > 2, and let K be a finite totally ramified extension over W (k)[ ] 1 pof ramification degreee. LetR0 be a relative base ring over W (k)〈t±1 1, …, tm±1〉 satisfying some mild conditions, and let R = R0 ⊗W (k) O ( [K . We show that if e < p−1, then every crystalline representation of π1étSpecR1 ]) p with Hodge–Tate weights in [0, 1] arises from a p-divisible group over R.