### The K-theory associated to a finite field I, by Daniel Quillen

This preprint of Quillen's was a preliminary unpublished version of the work
that was eventually published as "On the cohomology and K-theory of the general
linear groups over a finite field", Ann. of Math. 96 (1972) 552-586. The main
result concerns the homology of general linear groups over a finite field with
finite coefficients prime to the characteristic, with an eye toward the
computation of the K-groups of finite fields, to be accomplished in later
papers. The direct sum representation ring appears side by side with the exact
sequence representation ring in some of the arguments.

An alternative proof of a lemma is written in Kervaire's hand on the last page.

[ Thanks to Bruno Kahn for scanning the preprint; posted by Dan Grayson. The djvu
file comes with OCR text. ]

Daniel Quillen <none>