On the finite generation of additive group invariants in positive characteristic

Details On the finite generation of additive group invariants in positive characteristic On the finite generation of additive group invariants in positive characteristic

2010-01-19

arxiv.org/abs/1001.3293v2

Mathematics

Commutative Algebra

added a missing reference and a new section with an extension of the main result, corrected some typos, 14 pages

Scientific paper

Roberts, Freudenburg, and Daigle and Freudenburg have given the smallest counterexamples to Hilbert's fourteenth problem as rings of invariants of algebraic groups. Each is of an action of the additive group on a finite dimensional vector space over a field of characteristic zero, and thus, each is the kernel of a locally nilpotent derivation. In positive characteristic, additive group actions correspond to locally finite iterative higher derivations. We set up characteristic-free analogs of the three examples, and show that, contrary to characteristic zero, in every positive charateristic, the invariants are finitely generated.

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