
TL;DR
This paper constructs examples in algebraic group cohomology demonstrating unbounded extension dimensions and exponential growth of cohomology dimensions, answering two open questions for the case G=SL_2.
Contribution
It provides explicit examples showing unbounded Ext^2 dimensions and exponential growth of cohomology in algebraic groups, addressing open questions by Parshall and Scott.
Findings
xt_G^2(L,L) can be arbitrarily large
The sequence x_{L- ext{irred}} ext{dim} H^k(G,L) grows exponentially
Answers two open questions for G=SL_2
Abstract
We produce examples in the cohomology of algebraic groups which answer two questions of Parshall and Scott. Specifically, if , then we show: (a) can be arbitrarily large for a simple module ; and (b) the sequence grows exponentially fast with .
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Taxonomy
TopicsGender Studies in Language
