This project cooperates with TMR Network ERB FMRX CT-97-0107
Objectives: The aim of this project is to investigate reductive groups over arbitrary fields and asscociated linear and homological structures. Related linear structures are for example Lie algebras, Azumaya algebras, Jordan algebras, associative algebras with involution, quadratic and hermitean forms, related homological structures are those (co)homological functors and tools which are used or can be used to study those objects. Among them are the Galois or etale cohomology ring (e.g of a field or of a scheme), the cohomology functors describing Lie algebras, the Witt ring describing quadratic forms, the functors of algebraic K-theory and so on. More specialized objects in this context are e.g. the Brauer group of a field or of a variety, which is a particular instance of the functors being subsummized in the Galois cohomology ring of that object.