An integrality theorem of Grosshans over arbitrary base ring

Abstract

We revisit a theorem of Grosshans and show that it holds over arbitrary commutative base ring $k$. One considers a split reductive group scheme $G$ acting on a $k$-algebra $A$ and leaving invariant a subalgebra $R$. If $R^U=A^U$ then the conclusion is that $A$ is integral over $R$.

5 pages; final version

References in corpus (1)

• Power reductivity over an arbitrary base

Cited by in corpus (1)

• Reductivity properties over an affine base