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  "body": "\n## Summary\n\nA global field is either a [[number field|MWBDFS2KJ5]] or a global function field.\nA number field is a finite extension of $\\Q$, and a global function field is a finite extension of $\\F_q(t)$ for a finite field $\\F_q$.\nThe two kinds share much of their arithmetic: rings of integers, class groups, the product formula, adeles and [[class field theory|BEKCEYHCHX]].\nTheir completions at places are the [[local fields|J85FZEQG38]].\n\n## Explanations\n\n### L1 human\n\nThe rational numbers $\\Q$ and the rational functions $\\F_p(t)$ over a finite field behave alike in many ways.\nIn both, there is a notion of prime, unique factorization in a suitable ring, and many absolute values.\nA global field is a finite extension of one of these two basic fields.\nFor example, $\\Q(i)$, the numbers $a + bi$ with $a, b$ rational, is a global field of the first kind.\nStudying both kinds side by side often helps: a hard question about numbers can have an easier twin about functions.\n",
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