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  "body": "\n## Summary\n\nA Shimura variety is a quotient of a Hermitian [[symmetric space|PAA93R4WYD]] by a congruence subgroup of a [[reductive group|2XS84PWE3S]] over $\\Q$.\nIt is viewed as an algebraic variety.\nThe family includes [[modular curves|T5W0CMS0DM]] and the Siegel moduli spaces of abelian varieties.\nShimura varieties are defined over number fields, and their cohomology carries both Galois actions and automorphic forms.\nThis makes them a main bridge in the Langlands program.\n\n## Explanations\n\n### L1 human\n\nThe upper half-plane, divided out by a group such as $\\mathrm{SL}_2(\\Z)$, gives a modular curve, which parametrizes elliptic curves.\nShimura varieties are the higher-dimensional versions of this picture.\nThey start from a symmetric space with a complex structure and divide it by an arithmetic group.\nAn example is the Siegel upper half-space of symmetric complex matrices with positive definite imaginary part.\nThe result is an algebraic variety that often parametrizes abelian varieties with extra structure.\nBecause it has a natural model over a number field, it links geometry, automorphic forms and Galois representations.\n",
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