正特征可加群不变量的有限生成
On the finite generation of additive group invariants in positive characteristic
摘要：
罗伯茨，弗罗伊登堡，戴格尔和弗罗伊登堡给出了希尔伯特第十四问题的最小反例作为代数群的不变量环。每个都是特征为零的域上的有限维向量空间上的加法群的作用，因此，每个都是局部幂零导子的核。在正特征中，加性群作用对应于局部有限迭代高阶导数。我们建立了这三个例子的无特征类似物，并表明，与特征零相反，在每一个正特征中，不变量都是随机生成的。
英文摘要：
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 charateristic, the invariants are finitely generated.
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