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.

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Kevin P. Knudson <>