Unbounding Ext

Abstract

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) $\dim \Ext_G^2(L,L)$ can be arbitrarily large for a simple module $L$; and (b) the sequence $\max_{L-\text{irred}}\dim H^k(G,L)$ grows exponentially fast with $k$.