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An integrality theorem of Grosshans over arbitrary base ring

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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. Let U be the unipotent radical of a split Borel subgroup scheme. If R U = A U then the conclusion is that A is integral over R.

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  1. Mathematisch Instituut, P.O. Box 80.010, 3508 TA, Utrecht, The Netherlands

    Wilberd van der Kallen

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  1. Wilberd van der Kallen
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Correspondence to Wilberd van der Kallen.

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Dedicated to the memory of T. A. Springer

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van der Kallen, W. An integrality theorem of Grosshans over arbitrary base ring. Transformation Groups 19, 283–287 (2014). https://doi.org/10.1007/s00031-013-9241-x

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  • DOI: https://doi.org/10.1007/s00031-013-9241-x

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