Mathematical Sciences: 1992 Summer Research Institute on 'Quadratic Forms and Division Algebras'

上世纪80年代的S，代数K理论和代数几何的发展，使二次型代数理论和有限维除代数理论这两个密切相关的学科受益匪浅。从历史上讲，这次会议的议题植根于数论。大多数主要问题和动因都有一定的理论渊源。在本世纪上半叶，这些学科随着现代代数数论的发展而蓬勃发展。二次型的局部-全局原理的发现与p-ady场的发展密切相关。此外，局部域和整体域上有限维除代数的分类与类域理论的发展密切相关。在过去的四十年里，这些学科中的每一门都宣布与数论有很大的独立。这个项目将支持1992年夏季二次型和除法代数研究所：与代数K理论和代数几何的联系(该系列的第四十个)，将于1992年7月6-24日在加州大学圣巴巴拉分校举行。暑期学院的主要课题是与有限维除代数和二次型代数理论密切相关的学科。预计将通过举办两个特别讲座系列来推动进一步的进展，一个致力于代数K-理论，另一个致力于代数几何。此外，将有两个主要主题的研究讲座，二次型和除法代数。学院的第一周将强调二次型，第三周将强调除法代数，第二周将强调两者，希望能刺激互动。

During the 1980's the closely related subjects of the algebraic theory of quadratic forms and the theory of finite- dimensional division algebras benefitted greatly from developments in algebraic K-theory and algebraic geometry. The topics of this conference, historically speaking, are rooted in number theory. Most of the main problems and motivation have number theoretic origins. In the first half of this century, these subjects blossomed with the development of modern algebraic number theory. The discovery of local-global principles for quadratic forms was bound up with the development of p-adic fields. Further, the classification of finite-dimensional division algebras over local and global fields was closely connected to the development of class field theory. In the past forty years, each of these subjects has declared much independence from number theory. This project will support the 1992 Summer Research Institute on Quadratic Forms and Division Algebras: Connections with Algebraic K-theory and Algebraic Geometry (the fortieth in the series) to be held from July 6 - 24, 1992 at the University of California, Santa Barbara. The primary topics of the summer institute are the closely related subjects of finite-dimensional division algebras and the algebraic theory of quadratic forms. Further progress is expected to be stimulated by holding two special lecture series, one devoted to algebraic K-theory and the other to algebraic geometry. In addition, there will be research lectures on the two principal themes, quadratic forms and division algebras. The first week of the institute will have quadratic forms emphasis, the third week will have division algebra emphasis, and the second week will emphasize both with the hope of stimulating interaction.