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  "body": "\n## Statement\n\nNot all algebraic groups are linear groups or abelian varieties; for instance, some group schemes occurring naturally in arithmetic geometry are neither. Chevalley's structure theorem asserts that every connected algebraic group is an extension of an abelian variety by a linear algebraic group. More precisely, if *K* is a perfect field, and *G* a connected algebraic group over *K*, then there exists a unique normal closed subgroup *H* in *G*, such that *H* is a connected linear algebraic group and *G*/*H* an abelian variety.\n",
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