LOCALISATION OF UNSTABLE A_p-ALGEBRAS AND SMITH THEORY

摘要

In [6] the Borel-Quillen localisation theorem [4,10] is reformulated to produce an expression for the modp cohomology of the fixed point set of a finite Zp-complex X in terms of the modp equivariant cohomology of X. Here Zp denotes the cyclic group of prime order p. This result contrasts with previous work where the localised cohomology of the fixed point set is obtained. The key to this extension is to localise in the category of unstable /lp-algebras, where Ap is the mod p Steenrod algebra. Many of the classical results concerning the co-homology of fixed point sets then become statements concerning this localisation process.