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A reductive group is an algebraic group $G$ over an algebraically closed field such that the unipotent radical of $G$ is trivial
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How to read the paper of Arthur on trace formula on general reductive groups
One of the best places to learn about trace formula, other than David Whitehouse's wonderful notes, are the notes by Erez Lapid Introductory notes on the trace formula.
Arthur's trace formula relies o …