Ext^s_{P}(F[k], G[k]) ---> \Ext^s_{F(q)}(F,G)is an isomophism for all large enough k and q. Here F[k] denotes F twisted by the Frobenious k times.

This theorem is an analogue of an old stability theorem of E.Cline, B.Parshall, L.Scott, and W.van der Kallen relating rational GL_m modules to GL(m,q) modules. These two theorems then combine with an observation of Friedlander and Suslin to show that, for all finite F,G in P, and all s, the natural map

Ext^s_{F(q)}(F,G) ---> Ext^s_{GL(m,q)}(F(V_m),G(V_m))is an isomorphism for all large enough m and q. Thus group cohomology of the finite general linear groups in the stable range (a.k.a. stable K-theory of Fq with twisted coefficients) has often been identified with (the more computable) MacLane cohomology.

- 0198.bib (271 bytes)
- kuhn.dvi (94736 bytes) [May 28, 1997]
- kuhn.dvi.gz (35350 bytes)
- kuhn.pdf (197027 bytes)
- kuhn.ps.gz (200866 bytes)

Nicholas J. Kuhn <njk4x@virginia.edu>