论文标题
线性代数群有良好的降低
Linear algebraic groups with good reduction
论文作者
论文摘要
本文是对猜想的调查，并在适当的基本场离散估值集中降低了还原的还原群体。直到最近，这个主题的关注程度很少，但是现在它似乎正在发展为（线性）代数群体在高维领域的新兴算术理论中的中心主题之一。本文的重点是主要猜想，主张在有限生成的字段上，给定还原群体形式的同构形式的有限类别，该字段在该领域的一组地方有很好的减少。该猜想与代数群体理论中的其他问题之间的各种联系（例如，对Galois共同体中全球到本地图的分析，属问题等）进行了详细讨论。该文章还简要审查了有关离散估值，代数群体形式和Galois的共同体的所需事实。
This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but now it appears to be developing into one of the central topics in the emerging arithmetic theory of (linear) algebraic groups over higher-dimensional fields. The focus of this article is on the Main Conjecture asserting the finiteness of the number of isomorphism classes of forms of a given reductive group over a finitely generated field that have good reduction at a divisorial set of places of the field. Various connections between this conjecture and other problems in the theory of algebraic groups (such as the analysis of the global-to-local map in Galois cohomology, the genus problem, etc.) are discussed in detail. The article also includes a brief review of the required facts about discrete valuations, forms of algebraic groups, and Galois cohomology.
