# An upper bound on the Abbes-Saito filtration for finite flat group schemes and applications - Mathematics > Number Theory

An upper bound on the Abbes-Saito filtration for finite flat group schemes and applications - Mathematics > Number Theory - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: 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 boundedby a simple linear function of the degree of \$G\$. Assume \$\cO K\$ has genericcharacteristic 0 and the residue field of \$\cO K\$ is perfect. Farguesconstructed the higher level canonical subgroups for a Barsotti-Tate group\$\cG\$ over \$\cO K\$ which is -not too supersingular-. As an application of ourbound, 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\$.

Autor: Yichao Tian

Fuente: https://arxiv.org/