有限平群格式的Abbes-Saito滤性的上界及其应用
An upper bound on the Abbes-Saito filtration for finite flat group schemes and applications
摘要：
设$\cO_K$是剩余特征$p>0$的完备离散赋值环，$G$是$\cO_K$上的有限平坦群概型，其阶为$p$的a次幂.本文证明了$G$的Abbes-Saito滤子被一个关于$G$的次数的简单线性函数有界.假设$\cO_K$具有通用特征0并且$\cO_K$的剩余字段是完美的。Fargues构造了$\cO_K$上的Barsotti-Tate群$\cG$的高阶典范子群，它“不是超奇异的”.作为该界的应用，我们证明了Fargues构造的$n\geq 2$水平的$\cG$的典范子群出现在$\cG$的$p^n$ -挠子群的Abbes-Saito滤子中.
英文摘要：
Let $\cO_K$ be a complete discrete valuation ring of residue characteristic $p>0$, and $G$ be a finite flat group scheme over $\cO_K$ of order a power of $p$. We prove in this paper that the Abbes-Saito filtration of $G$ is bounded by a simple linear function of the degree of $G$. Assume $\cO_K$ has generic characteristic 0 and the residue field of $\cO_K$ is perfect. Fargues constructed the higher level canonical subgroups for a Barsotti-Tate group $\cG$ over $\cO_K$ which is "not too supersingular". As an application of our bound, we prove that the canonical subgroup of $\cG$ of level $n\geq 2$ constructed by Fargues appears in the Abbes-Saito filtration of the $p^n$-torsion subgroup of $\cG$.
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