论文标题
与log 1-Motives关联的日志P分组
Log p-divisible groups associated to log 1-motives
论文作者
论文摘要
我们首先提供了Kato在Noetherian Henselian本地戒指上的日志$ P $可分类组的分类定理的详细证明。然后，我们进一步探索了Kato的想法，然后定义了经典有限有限的平面集团计划（分别是经典的$ P $ - P $ -Divisible Group）在有限的Kummer log flat flat log of to progim offiv $ p的类别中，通过经典有限的平面组计划（分别进行经典$ p $ -Divivisible组）来定义了经典有限的典型$ p $ - 可划分组的标准扩展概念。然后使用这些结果证明log $ p $ - 可分别的组正式登录光滑。然后，我们研究有限的kummer平面日志计划$ t_n（\ Mathbf {m}）：= h^{ - 1}（\ Mathbf {M} \ otimes _ {\ Mathbb {Z}}}^l \ Mathbb {Z}/n \ Mathbb {Z}/n \ Mathbb {Z} $ PROGIS $ \ mathbf {m} [p^{\ infty}] $）在FS日志方案上的日志1-Motive $ \ Mathbf {M Mathbf {M Mathbf {M} $，并表明它们是本地标准扩展。最后，我们给出了以恒定变性的对数阿贝尔品种的Serre-Tate定理的证明。
We first provide a detailed proof of Kato's classification theorem of log $p$-divisible groups over a noetherian henselian local ring. Exploring Kato's idea further, we then define the notion of a standard extension of a classical finite étale group scheme (resp. classical étale $p$-divisible group) by a classical finite flat group scheme (resp. classical $p$-divisible group) in the category of finite Kummer flat group log schemes (resp. log $p$-divisible groups), with respect to a given chart on the base. These results are then used to prove that log $p$-divisible groups are formally log smooth. We then study the finite Kummer flat group log schemes $T_n(\mathbf{M}):=H^{-1}(\mathbf{M}\otimes_{\mathbb{Z}}^L\mathbb{Z}/n\mathbb{Z})$ (resp. the log $p$-divisible group $\mathbf{M}[p^{\infty}]$) of a log 1-motive $\mathbf{M}$ over an fs log scheme and show that they are étale locally standard extensions. Lastly, we give a proof of the Serre-Tate theorem for log abelian varieties with constant degeneration.
