On the finite generation of additive group invariants in positive characteristic

• Verfasst von: Dufresne, Emilie [VerfasserIn]
• Verfasst von: Maurischat, Andreas [VerfasserIn]
• Titel: On the finite generation of additive group invariants in positive characteristic
• Verf.angabe: Emilie Dufresne, Andreas Maurischat
• Umfang: 12 S.
• Fussnoten: Gesehen am 21.02.2019
• Titel Quelle: Enthalten in: Journal of algebra
• Jahr Quelle: 2010
• Band/Heft Quelle: 324(2010), 8, S. 1952-1963
• ISSN Quelle: 1090-266X
• DOI: doi:10.1016/j.jalgebra.2010.05.023
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1587892979

Abstract

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.