Class groups and general linear group cohomology for a ring of algebraic integers, by Stephen A. Mitchell

Let R be the ring of integers in an algebraic number field, with an odd prime p inverted. We define a certain polynomial Hopf algebra in terms of the class group of R and show that it is a retract of the mod p cohomology of the infinite general linear group GL(R). We show further that this polynomial algebra is precisely the quotient of the cohomology of GL(R) obtained by factoring out the ideal of all elements whose restriction to each GL(n,R) is nilpotent.


Stephen A. Mitchell <mitchell@math.washington.edu>