A Remark on Torsors under Affine Group Schemes

Torsors under smooth group-schemes and Morava stabilizer groups

For every prime p and integer n > 3 we explicitly construct an abelian variety A/Fpn of dimension n such that for a suitable prime l the group of quasi-isogenies of A/Fpn of l-power degree is canonically a dense subgroup of the n-th Morava stabilizer group at p. We also give a variant of this result taking into account a polarization. This is motivated by the recent construction of topological ...

One - Dimensional Affine Group Schemes

The construction of these groups is straightforward; to an algebra B we assign the quotient R,,, G,/G,. The main effort comes in showing that these are the only possibilities. The key to this, and the basic technical idea in the paper, is the use of N&on blow-ups of group schemes over valuation rings. This process has been used before [ 1, 21 as a tool for resolving singularities, but in fact i...

Torsors over the Punctured Affine Line

We classify G-torsors over the punctured affine line Spec (k[t]) where G is a reductive algebraic group defined over a field k of good characteristic. Our classification is in terms of the Galois cohomology of the complete field k((t)) with values in G.

Basic Theory of Affine Group Schemes

On Codes that are Invariant under the Affine Group

Let k[V ] be the space of functions from a finite vector space into the algebraically closure of its field of scalars. This paper describes the lattice of subspaces of k[V ] which are invariant under the affine group AGL(V ). The description provides a simple method for finding the submodule generated by any set of functions given as polynomials in the standard coordinates.