Factorisation properties of group scheme actions

Details Factorisation properties of group scheme actions Factorisation properties of group scheme actions

2010-08-25

arxiv.org/abs/1008.4292v3

Mathematics

Commutative Algebra

Scientific paper

Let H be an algebraic group scheme over a field k acting on a commutative
k-algebra A which is a unique factorisation domain. We show that, under certain
mild assumptions, the monoid of nonzero H-stable principal ideals in A is free
commutative. From this we deduce, in certain special cases, results about the
monoid of nonzero semi-invariants and the algebra of invariants.

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