Integral homology of PGL2 over elliptic curves, by Kevin P. Knudson

In this note we compute the homology of PGL2(A), where A is the coordinate ring of an elliptic curve defined by some Weierstrass equation (i.e., the curve has a unique point at infinity). We assume our ground field is infinite. For each i>0, the group Hi consists of a number direct summands of the form Hi(PGL2(k)) and summands of the form Hi(k*) as well as a few additional summands in certain cases. If k is algebraically closed, we derive a rigidity statement as a corollary.

The files no.ps, unique.ps and distinct.ps are postscript files containing illustrations for the paper. Dvips knows how to use them when processing elliptic.dvi. If you download elliptic.ps, you don't need those other files. Each file also comes in a compressed version, whose name ends with .gz.


Kevin P. Knudson <knudson@math.nwu.edu>