On lower ramification subgroups and canonical subgroups

Canonical Subgroups of H

Canonical and filling subgroups of formal groups

Let F be a one-dimensional full or almost full p-adic formal group. We look for finite subgroups C of F for which the quotient formal group F/C is full. In particular, we investigate the connection between such groups and the congruence-torsion subgroups of F described in Lubin, 1979. In doing so, we prove a conjecture of Jonathan Lubin concerning this relationship when F

Canonical Subgroups of Barsotti-tate Groups

Let S be the spectrum of a complete discrete valuation ring with fraction field of characteristic 0 and perfect residue field of characteristic p ≥ 3. Let G be a truncated BarsottiTate group of level 1 over S. If “G is not too supersingular”, a condition that will be explicitly expressed in terms of the valuation of a certain determinant, we prove that we can canonically lift the kernel of the ...

Higher-level Canonical Subgroups in Abelian Varieties

1.1. Motivation. Let E be an elliptic curve over a p-adic integer ring R, and assume that E has supersingular reduction. Consider the 2-dimensional Fp-vector space of characteristic-0 geometric p-torsion points in the associated 1-parameter formal group Ê over R. It makes sense to ask if, in this vector space, there is a line whose points x are nearer to the origin than are all other points (wi...

Smarandache algebras and their subgroups

In this paper we define S algebras and show that every finite group can be found in some S algebra.  We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.