UNIPOTENT GROUP SCHEMES OVER INTEGRAL RINGS
UNIPOTENT GROUP SCHEMES OVER INTEGRAL RINGS
复制标题
积分环上的单能群方案
DOI：
--
复制
发表时间：
1974
期刊：
影响因子：
--
通讯作者：
I. V. Dolgačëv
中科院分区：
文献类型：
--
作者：
B. J. Veisfeiler;I. V. Dolgačëv
本文研究整环上的幂幺代数群族。主要结果涉及到这样的家庭的几何形状。特别地，我们证明了在某些假设下，这样的族的空间同构于基上的仿射空间。我们给出的反例表明，在任意基环的情况下，域上的幂幺代数群理论的基本事实不再成立。对于某一类的组计划，我们认为我们证明结果上同调，扩展和变形。
In this paper we study families of unipotent algebraic groups over integral rings. The main results relate to the geometry of such families. In particular, we prove that, under some hypotheses, the space of such a family is isomorphic to an affine space over the base. We give counterexamples showing that in the case of an arbitrary base ring the basic facts of the theory of unipotent algebraic groups over a field cease to be true. For a certain class of the group schemes that we consider we prove results on cohomology, extensions and deformations.