Power reductivity over an arbitrary base

Details Power reductivity over an arbitrary base Power reductivity over an arbitrary base

2008-06-04

arxiv.org/abs/0806.0787v2

Documenta Mathematica - Extra Volume Suslin (2010)

Mathematics

Representation Theory

24 p; Some finiteness results added for rational cohomology over the integers

Scientific paper

Our starting point is Mumford's conjecture, on representations of Chevalley groups over fields, as it is phrased in the preface of "Geometric Invariant Theory". After extending the conjecture appropriately, we show that it holds over an arbitrary commutative base ring. 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 deformation of an algebra in the same generality. We end with tentative finiteness results for rational cohomology over the integers.

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