On the finite generation of additive group invariants in positive characteristic

JOURNAL OF ALGEBRA

卷:324

Article

Dufresne, Emilie¹  Maurischat, Andreas² 

[1] Univ Heidelberg, Math Ctr Heidelberg, D-69120 Heidelberg, Germany

[2] Univ Heidelberg, Interdisciplinary Ctr Sci Comp IWR, D-69120 Heidelberg, Germany

关键词: Hilbert's fourteenth problem;    Locally finite iterative higher derivations;   

DOI  :  10.1016/j.jalgebra.2010.05.023

来源: Elsevier

【 摘 要 】

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 characteristic, the invariants are finitely generated. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free