Log <i>p</i>-divisible groups associated with log 1-motives

Abstract We first provide a detailed proof of Kato’s classification theorem log p -divisible groups over Noetherian Henselian local ring. Exploring idea further, we then define the notion standard extension classical finite étale group scheme (resp. group) by flat in category Kummer schemes groups), with respect to given chart on base. These results are used prove that formally smooth. study $T_n(\mathbf {M}):=H^{-1}(\mathbf {M}\otimes _{{\mathbb Z}}^L{\mathbb Z}/n{\mathbb Z})$ $\mathbf {M}[p^{\infty }]$ ) 1-motive {M}$ an fs and show they locally extensions. Lastly, give Serre–Tate for abelian varieties constant degeneration.