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  "body": "\n## Summary\n\nAn arithmetic group is a group of integer matrices cut out by polynomial equations, such as $\\mathrm{SL}_n(\\Z)$.\nA group that agrees with such a group up to finite index is also arithmetic.\nArithmetic groups link number theory with the geometry of Lie groups.\nFor a semisimple group, a theorem of Borel and Harish-Chandra says that the arithmetic subgroups are lattices in the real Lie group.\nThe Margulis arithmeticity theorem shows that in higher rank all irreducible lattices arise this way.\n\n## Explanations\n\n### L1 human\n\nTake a group of real matrices defined by equations, such as the matrices of determinant $1$.\nKeep only the matrices whose entries are integers.\nThe result, such as $\\mathrm{SL}_2(\\Z)$, is an arithmetic group.\nIt sits inside the big continuous group like the integer points $\\Z^2$ sit inside the plane $\\R^2$.\nThe [[modular group|VEKV1EM77B]] $\\mathrm{SL}_2(\\Z)$, which acts on the upper half plane, is the most famous example.\n",
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