Unbounding Ext

We produce examples in the cohomology of algebraic groups which answer two questions of Parshall and Scott. Specifically, if G=SL ₂, then we show: (a) dimExtG2(L,L) can be arbitrarily large for a simple module L; and (b) if we define γ _m=max _LdimH ^m(G, L) where the maximum is taken over all simple G-modules L, then the sequence {γ _m} grows exponentially fast with m.