Filtration of elliptic-curve points over a local field
= Filtration of elliptic-curve points over a local field
For an elliptic curve over a nonarchimedean local field, $E_0$ consists of points with nonsingular reduction, $E_1$ is the kernel of reduction, and $E_r$ for $r\geq1$ consists of points whose formal parameter has valuation at least $r$. The successive quotients for $r\geq1$ are copies of the additive residue-field group.