Power reductivity over an arbitrary base

Vincent Franjou (1) , Wilberd van Der Kallen (2)

1 Topologie, géométrie et algèbre
2 Utrecht Mathematical Institute

We prove a straight generalization to an arbitrary base of Mumford's conjecture on Chevalley groups over fields. We thus obtain the first fundamental theorem of invariant theory (often referred to as Hilbert's fourteenth problem) over an arbitrary Noetherian ring. We also prove results on the Grosshans graded of an algebra in the same generality.

Mots clés: Chevalley group; algebraic group; group scheme; reductive; invariant; ring; cohomology; Grosshans filtration; Hilbert; finitely generated algebra; determinant; Steinberg module; weight; good filtration

Domaines: Théorie des représentations [math.RT]

Vincent Franjou, Wilberd van Der Kallen. Power reductivity over an arbitrary base. 2008. ⟨hal-00284888⟩