论文标题
Nilpotent群体对复杂代数品种的作用
Actions of nilpotent groups on complex algebraic varieties
论文作者
论文摘要
我们研究忠实地针对复杂代数品种的nilpotent群体。我们使用基本变化的方法。对于有限的P组，我们从$ k $（一个数字字段）转到有限字段，以便使用计数诱饵。我们表明，$ k^d $的多项式自动形态的有限$ p $ - 与gl $ _d（k）$的子组同构。对于无限组，我们从$ \ mathbb {c} $转到$ \ mathbb {z} _p $，并使用p-adic分析工具和p-adic lie lie groups的理论。我们表明，有限生成的nilpotent $ h $忠实地在复杂的quasiprojective品种$ x $ dimension $ d $上嵌入到$ p $ ad的谎言组中，忠实地和分析地在$ \ mathbb {z} _p^_p^d $上忠实地行动；我们推断出$ d $大于$ h $的虚拟派生长度。
We study nilpotent groups acting faithfully on complex algebraic varieties. We use a method of base change. For finite p-groups, we go from $k$, a number field, to a finite field in order to use counting lemmas. We show that a finite $p$-group of polynomial automorphisms of $k^d$ is isomorphic to a subgroup of GL$_d(k)$. For infinite groups, we go from $\mathbb{C}$ to $\mathbb{Z}_p$ and use p-adic analytic tools and the theory of p-adic Lie groups. We show that a finitely generated nilpotent group $H$ acting faithfully on a complex quasiprojective variety $X$ of dimension $d$ can be embedded into a $p$-adic Lie group acting faithfully and analytically on $\mathbb{Z}_p^d$; we deduce that $d$ is larger than the virtual derived length of $H$.
