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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 $ngeq 2$ constructed by Fargues appears in the Abbes-Saito filtration of the $p^n$-torsion subgroup of $cG$.
Let $p$ be a prime. Let $V$ be a discrete valuation ring of mixed characteristic $(0,p)$ and index of ramification $e$. Let $f: G rightarrow H$ be a homomorphism of finite flat commutative group schemes of $p$ power order over $V$ whose generic fiber
Let $G$ be a finite (not necessarily abelian) group and let $p=p(G)$ be the smallest prime number dividing $|G|$. We prove that $d(G)leq frac{|G|}{p}+9p^2-10p$, where $d(G)$ denotes the small Davenport constant of $G$ which is defined as the maximal
A subset ${g_1, ldots , g_d}$ of a finite group $G$ invariably generates $G$ if the set ${g_1^{x_1}, ldots, g_d^{x_d}}$ generates $G$ for every choice of $x_i in G$. The Chebotarev invariant $C(G)$ of $G$ is the expected value of the random variable
A p-divisible group, or more generally an F-crystal, is said to be Hodge-Newton reducible if its Hodge polygon passes through a break point of its Newton polygon. Katz proved that Hodge-Newton reducible F-crystals admit a canonical filtration called
We prove that there is a natural plectic weight filtration on the cohomology of Hilbert modular varieties in the spirit of Nekovar and Scholl. This is achieved with the help of Morels work on weight t-structures and a detailed study of partial Froben