An Algebraic Periodicity Theorem for Spheres

Joseph P. Brennan
1984 Proceedings of the American Mathematical Society  
A periodicity theorem is given for spheres over a field of finite level generalizing results of Jouanolou. An extension of this result gives families of smooth affine varities with isomorphic A"-groups. The Bott periodicity theorem [1] lies at the foundation of topological ÄT-theory. In particular, it yields the fact that the real and complex topological AT-groups of spheres are periodic in the dimension. Consequent to work of Fossum [2] and Jouanolou [4] , it was noted that the algebraic
more » ... the algebraic ÄT0-groups of complex spheres were isomorphic to the topological ÄT-groups hence they enjoyed periodic behavior. Later Jouanolou [5] showed that if -1 is a square in the field k and if Xn =
doi:10.2307/2045342 fatcat:gyf537vqajhthmll75ldsz2gvy