Invariant deformation theory of affine schemes with reductive group action

Moduli of Affine Schemes with Reductive Group Action

For a connected reductive group G and a finite–dimensional G–module V , we study the invariant Hilbert scheme that parameterizes closed G–stable subschemes of V affording a fixed, multiplicity–finite representation of G in their coordinate ring. We construct an action on this invariant Hilbert scheme of a maximal torus T of G, together with an open T–stable subscheme admitting a good quotient. ...

Basic Theory of Affine Group Schemes

Reductive Group Schemes

— We develop the relative theory of reductive group schemes, using dynamic techniques and algebraic spaces to streamline the original de-

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...

Reductive Group Schemes (sga3 Summer School, 2011)

The aim of these notes is to develop the theory of reductive group schemes, incorporating some simplifications into the methods of [SGA3]. We assume the reader is familiar with the basic structure theory over an algebraically closed field k (as developed in [Bo91], [Hum87], [Spr]), but a review is given in §1 in order to fix our terminology, set everything in the framework of k-schemes (rather ...