[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/292059#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/292059","headline":"\u30a2\u30c7\u30fc\u30eb\u4ee3\u6570\u7fa4 – Wikipedia","name":"\u30a2\u30c7\u30fc\u30eb\u4ee3\u6570\u7fa4 – Wikipedia","description":"\u62bd\u8c61\u4ee3\u6570\u5b66\u306b\u304a\u3044\u3066\uff0c\u30a2\u30c7\u30fc\u30eb\u4ee3\u6570\u7fa4\uff08\u30a2\u30c7\u30fc\u30eb\u3060\u3044\u3059\u3046\u3050\u3093\uff0c\u82f1: adelic algebraic group\uff09\u306f\u6570\u4f53 K \u4e0a\u306e\u4ee3\u6570\u7fa4 G \u3068 K \u306e\u30a2\u30c7\u30fc\u30eb\u74b0 A = A(K) \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u534a\u4f4d\u76f8\u7fa4\uff08\u82f1\u8a9e\u7248\uff09\u3067\u3042\u308b\uff0e\u305d\u308c\u306f\u3001\u4ee3\u6570\u7fa4 G \u306e A-\u5024\u70b9\u5168\u3066\u304b\u3089\u306a\u308b\uff1b\u9069\u5207\u306a\u4f4d\u76f8\u306e\u5b9a\u7fa9\u306f G \u304c\u7dda\u578b\u4ee3\u6570\u7fa4\u306e\u3068\u304d\u306b\u9650\u308a\u7c21\u5358\u3067\u3042\u308b\uff0eG \u304c\u30a2\u30fc\u30d9\u30eb\u591a\u69d8\u4f53\u306e\u3068\u304d\u306b\u306f\u305d\u308c\u306f\u6280\u8853\u7684\u306a\u969c\u5bb3\u3092\u8868\u3059\uff0e\u6982\u5ff5\u306f\u6f5c\u5728\u7684\u306b\u306f\u7389\u6cb3\u6570\u3068\u306e\u95a2\u4fc2\u3067\u6709\u7528\u3067\u3042\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u306f\u3044\u308b\u304c\uff0e\u30a2\u30c7\u30fc\u30eb\u4e0a\u306e\u4ee3\u6570\u7fa4\u306f\u6570\u8ad6\u306b\u304a\u3044\u3066\u5e83\u304f\u7528\u3044\u3089\u308c\uff0c\u7279\u306b\u4fdd\u578b\u8868\u73fe\u8ad6\u3068\u4e8c\u6b21\u5f62\u5f0f\u306e\u6570\u8ad6\u306b\u304a\u3044\u3066\u7528\u3044\u3089\u308c\u308b\uff0e","datePublished":"2022-04-26","dateModified":"2022-04-26","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/ja.wikipedia.org\/wiki\/Special:CentralAutoLogin\/start?type=1x1","url":"https:\/\/ja.wikipedia.org\/wiki\/Special:CentralAutoLogin\/start?type=1x1","height":"1","width":"1"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/292059","about":["wiki"],"wordCount":2361,"articleBody":"\u62bd\u8c61\u4ee3\u6570\u5b66\u306b\u304a\u3044\u3066\uff0c\u30a2\u30c7\u30fc\u30eb\u4ee3\u6570\u7fa4\uff08\u30a2\u30c7\u30fc\u30eb\u3060\u3044\u3059\u3046\u3050\u3093\uff0c\u82f1: adelic algebraic group\uff09\u306f\u6570\u4f53 K \u4e0a\u306e\u4ee3\u6570\u7fa4 G \u3068 K \u306e\u30a2\u30c7\u30fc\u30eb\u74b0 A = A(K) \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u534a\u4f4d\u76f8\u7fa4\uff08\u82f1\u8a9e\u7248\uff09\u3067\u3042\u308b\uff0e\u305d\u308c\u306f\u3001\u4ee3\u6570\u7fa4 G \u306e A-\u5024\u70b9\u5168\u3066\u304b\u3089\u306a\u308b\uff1b\u9069\u5207\u306a\u4f4d\u76f8\u306e\u5b9a\u7fa9\u306f G \u304c\u7dda\u578b\u4ee3\u6570\u7fa4\u306e\u3068\u304d\u306b\u9650\u308a\u7c21\u5358\u3067\u3042\u308b\uff0eG \u304c\u30a2\u30fc\u30d9\u30eb\u591a\u69d8\u4f53\u306e\u3068\u304d\u306b\u306f\u305d\u308c\u306f\u6280\u8853\u7684\u306a\u969c\u5bb3\u3092\u8868\u3059\uff0e\u6982\u5ff5\u306f\u6f5c\u5728\u7684\u306b\u306f\u7389\u6cb3\u6570\u3068\u306e\u95a2\u4fc2\u3067\u6709\u7528\u3067\u3042\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u306f\u3044\u308b\u304c\uff0e\u30a2\u30c7\u30fc\u30eb\u4e0a\u306e\u4ee3\u6570\u7fa4\u306f\u6570\u8ad6\u306b\u304a\u3044\u3066\u5e83\u304f\u7528\u3044\u3089\u308c\uff0c\u7279\u306b\u4fdd\u578b\u8868\u73fe\u8ad6\u3068\u4e8c\u6b21\u5f62\u5f0f\u306e\u6570\u8ad6\u306b\u304a\u3044\u3066\u7528\u3044\u3089\u308c\u308b\uff0e  G \u304c\u7dda\u578b\u4ee3\u6570\u7fa4\u306e\u3068\u304d\uff0c\u305d\u308c\u306f\u30a2\u30d5\u30a1\u30a4\u30f3 N-\u7a7a\u9593\u306b\u304a\u3051\u308b\u30a2\u30d5\u30a1\u30a4\u30f3\u4ee3\u6570\u591a\u69d8\u4f53\u3067\u3042\u308b\uff0e\u30a2\u30c7\u30fc\u30eb\u4ee3\u6570\u7fa4 G(A) \u4e0a\u306e\u4f4d\u76f8\u306f\u30a2\u30c7\u30fc\u30eb\u74b0\u306e N \u500b\u306e\u30b3\u30d4\u30fc\u306e\u30c7\u30ab\u30eb\u30c8\u7a4d AN \u306e\u90e8\u5206\u7a7a\u9593\u4f4d\u76f8\u304c\u53d6\u3089\u308c\u308b\uff0eTable of Contents\u30a4\u30c7\u30fc\u30eb[\u7de8\u96c6]\u7528\u8a9e\u306e\u6b74\u53f2[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]\u30a4\u30c7\u30fc\u30eb[\u7de8\u96c6]\u91cd\u8981\u306a\u4f8b\u3067\u3042\u308b\u30a4\u30c7\u30fc\u30eb\u7fa4 (idele group) I(K) \u306f G = GL1 \u306e\u5834\u5408\u3067\u3042\u308b\uff0e\u3053\u3053\u3067\u30a4\u30c7\u30fc\u30eb\uff08idele \u3042\u308b\u3044\u306f id\u00e8le, \uff09\u306e\u96c6\u5408\u306f\u53ef\u9006\u306a\u30a2\u30c7\u30fc\u30eb\u306e\u5168\u4f53\u304b\u3089\u306a\u308b\uff1b\u3057\u304b\u3057\u30a4\u30c7\u30fc\u30eb\u7fa4\u306e\u4f4d\u76f8\u306f\u30a2\u30c7\u30fc\u30eb\u306e\u90e8\u5206\u96c6\u5408\u3068\u3057\u3066\u306e\u4f4d\u76f8\u3067\u306f\u306a\u3044\uff0e\u305d\u3046\u3067\u306f\u306a\u304f\uff0cGL1 \u304c2\u6b21\u5143\u30a2\u30d5\u30a3\u30f3\u7a7a\u9593\u306b\u304a\u3044\u3066 {(t, t\u22121)} \u306b\u3088\u3063\u3066\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306b\u5b9a\u7fa9\u3055\u308c\u305f’\u53cc\u66f2\u7dda’\u3068\u3057\u3066\u5165\u3063\u3066\u3044\u308b\u3068\u8003\u3048\u3066\uff0c\u30a4\u30c7\u30fc\u30eb\u7fa4\u306b\u6b63\u3057\u304f\u5272\u308a\u5f53\u3066\u3089\u308c\u305f\u4f4d\u76f8\u306f A2 \u3078\u306e\u5305\u542b\u304b\u3089\u8a98\u5c0e\u3055\u308c\u308b\u3082\u306e\u3067\u3042\u308b\uff1b\u5c04\u5f71\u3068\u5408\u6210\u3057\u3066\uff0c\u30a4\u30c7\u30fc\u30eb\u306f A \u306e\u90e8\u5206\u7a7a\u9593\u4f4d\u76f8\u3088\u308a\u3082\u7d30\u304b\u3044\u4f4d\u76f8\uff08\u82f1\u8a9e\u7248\uff09\u3092\u6301\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u5f93\u3046\uff0e  AN \u306e\u4e2d\u306b\u7a4d KN \u306f\u96e2\u6563\u90e8\u5206\u7fa4\u3068\u3057\u3066\u5165\u3063\u3066\u3044\u308b\uff0e\u3053\u308c\u306f G(K) \u304c G(A) \u306e\u96e2\u6563\u90e8\u5206\u7fa4\u3067\u3042\u308b\u3053\u3068\u3082\u610f\u5473\u3059\u308b\uff0e\u30a4\u30c7\u30fc\u30eb\u7fa4\u306e\u5834\u5408\u306b\u306f\uff0c\u5546\u7fa4I(K)\/K\u00d7\u306f\u30a4\u30c7\u30fc\u30eb\u985e\u7fa4\u3067\u3042\u308b\uff0e\u3053\u308c\u306f\u30a4\u30c7\u30a2\u30eb\u985e\u7fa4\u3068\u5bc6\u63a5\u306b\u95a2\u4fc2\u3057\u3066\u3044\u308b\uff08\u3088\u308a\u5927\u304d\u3044\u304c\uff09\uff0e\u30a4\u30c7\u30fc\u30eb\u985e\u7fa4\u306f\u305d\u308c\u81ea\u8eab\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u306f\u306a\u3044\uff1b\u30a4\u30c7\u30fc\u30eb\u306f\u307e\u305a\u30ce\u30eb\u30e0 1 \u306e\u30a4\u30c7\u30fc\u30eb\u3067\u7f6e\u304d\u63db\u3048\u3089\u308c\u306a\u3051\u308c\u3070\u306a\u3089\u305a\uff0c\u3059\u308b\u3068\u30a4\u30c7\u30fc\u30eb\u985e\u7fa4\u306b\u304a\u3051\u308b\u305d\u308c\u3089\u306e\u50cf\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u7fa4\u3067\u3042\u308b\uff1b\u3053\u308c\u306e\u8a3c\u660e\u306f\u985e\u6570\u306e\u6709\u9650\u6027\u3068\u672c\u8cea\u7684\u306b\u540c\u5024\u3067\u3042\u308b\uff0e\u30a4\u30c7\u30fc\u30eb\u985e\u7fa4\u306e\u30ac\u30ed\u30ef\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u306e\u7814\u7a76\u306f\u985e\u4f53\u8ad6\u306b\u304a\u3044\u3066\u4e2d\u5fc3\u7684\u306a\u4e8b\u67c4\u3067\u3042\u308b\uff0e\u30a4\u30c7\u30fc\u30eb\u985e\u7fa4\u306e\u6307\u6a19\u306f\uff0c\u4eca\u3067\u306f\u901a\u5e38\u30d8\u30c3\u30b1\u6307\u6a19\u3068\u547c\u3070\u308c\u308b\u304c\uff0cL \u95a2\u6570\u306e\u6700\u3082\u57fa\u672c\u7684\u306a\u30af\u30e9\u30b9\u3092\u751f\u3058\u308b\uff0e\u3088\u308a\u4e00\u822c\u306e G \u306b\u5bfe\u3057\u3066\uff0c\u7389\u6cb3\u6570\u306f G(A)\/G(K) \u306e\u6e2c\u5ea6\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\uff08\u3042\u308b\u3044\u306f\u9593\u63a5\u7684\u306b\u8a08\u7b97\u3055\u308c\u308b\uff09\uff0e  \u7389\u6cb3\u6052\u592b\u306e\u89b3\u5bdf\u306f K \u4e0a\u5b9a\u7fa9\u3055\u308c\u305f G \u4e0a\u306e\u4e0d\u5909\u5fae\u5206\u5f62\u5f0f \u03c9 \u304b\u3089\u59cb\u3081\u3066\u95a2\u4fc2\u3057\u305f\u6e2c\u5ea6\u304c well-defined \u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3060\u3063\u305f\uff1a\u03c9 \u306f c \u3092 K \u306e\u975e\u96f6\u5143\u3068\u3057\u3066 c\u03c9 \u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3082\u3067\u304d\u308b\u304c\uff0cK \u306e\u4ed8\u5024\u306e\u7a4d\u516c\u5f0f\u306f\uff0c\u5404\u6709\u5411\u56e0\u5b50\u4e0a \u03c9 \u304b\u3089\u69cb\u6210\u3055\u308c\u305f\u7a4d\u6e2c\u5ea6\u306b\u5bfe\u3057\u3066\uff0c\u5546\u306e\u6e2c\u5ea6\u306e c \u304b\u3089\u306e\u72ec\u7acb\u6027\u3092\u53cd\u6620\u3059\u308b\uff0e\u534a\u5358\u7d14\u7fa4\uff08\u82f1\u8a9e\u7248\uff09\u306b\u5bfe\u3059\u308b\u7389\u6cb3\u6570\u306e\u8a08\u7b97\u306f\u53e4\u5178\u7684\u306a\u4e8c\u6b21\u5f62\u5f0f\u306e\u7406\u8ad6\u306e\u91cd\u8981\u306a\u90e8\u5206\u3092\u542b\u3080\uff0e\u7528\u8a9e\u306e\u6b74\u53f2[\u7de8\u96c6]\u6b74\u53f2\u7684\u306b\u306f id\u00e8le \u304c  Chevalley\u00a0(1936) \u306b\u3088\u3063\u3066 “\u00e9l\u00e9ment id\u00e9al”\uff08\u30d5\u30e9\u30f3\u30b9\u8a9e\u3067\u300c\u7406\u60f3\u5143\u300d\uff09\u306e\u540d\u306e\u4e0b\u3067\u5c0e\u5165\u3055\u308c\uff0cChevalley (1940) \u304c\u30cf\u30c3\u30bb\u306e\u63d0\u6848\u306b\u5f93\u3063\u3066 “id\u00e8le” \u306b\u7701\u7565\u3057\u305f\uff0e\uff08\u3053\u308c\u3089\u306e\u8ad6\u6587\u306b\u304a\u3044\u3066\u5f7c\u306f\u30cf\u30a6\u30b9\u30c9\u30eb\u30d5\u3067\u306a\u3044\u4f4d\u76f8\u306e\u30a4\u30c7\u30fc\u30eb\u3092\u4e0e\u3048\u308b\u3053\u3068\u3082\u3057\u305f\uff0e\uff09\u3053\u308c\u306f\u7121\u9650\u6b21\u62e1\u5927\u306b\u5bfe\u3057\u3066\u4f4d\u76f8\u7fa4\u306e\u3053\u3068\u3070\u3067\u985e\u4f53\u8ad6\u3092\u5b9a\u5f0f\u5316\u3059\u308b\u305f\u3081\u3067\u3042\u3063\u305f\uff0eWeil (1938) \u306f\u95a2\u6570\u4f53\u306e\u5834\u5408\u306b\u30a2\u30c7\u30fc\u30eb\u306e\u74b0\u3092\u5b9a\u7fa9\u3057\uff08\u305f\u304c\u540d\u3065\u3051\u306a\u304b\u3063\u305f\uff09\uff0cIdealelemente \u306e\u30b7\u30e5\u30d0\u30ec\u30fc\u306e\u7fa4\u304c\u3053\u306e\u74b0\u306e\u53ef\u9006\u5143\u306e\u7fa4\u3067\u3042\u308b\u3053\u3068\u3092\u6307\u6458\u3057\u305f\uff0eTate (1950) \u306f\u30a2\u30c7\u30fc\u30eb\u306e\u74b0\u3092\u5236\u9650\u76f4\u7a4d\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u305f\u304c\uff0c\u5f7c\u306f\u305d\u306e\u5143\u3092\u30a2\u30c7\u30fc\u30eb\u3067\u306f\u306a\u304f “valuation vector” \u3068\u547c\u3093\u3060\uff0eChevalley (1951) \u306f\u95a2\u6570\u4f53\u306e\u5834\u5408\u306b “repartitions” \u306e\u540d\u306e\u4e0b\u3067\u30a2\u30c7\u30fc\u30eb\u306e\u74b0\u3092\u5b9a\u7fa9\u3057\u305f\uff0e\u7528\u8a9e ad\u00e8le\uff08additive id\u00e8le \u306e\u7701\u7565\u3067\uff0c\u30d5\u30e9\u30f3\u30b9\u4eba\u5973\u6027\u306e\u540d\u524d\u3067\u3082\u3042\u308b\uff09\u306f\uff0c\u307e\u3082\u306a\u304f\u305d\u306e\u5f8c\u4f7f\u308f\u308c\u305f (Jaffard 1953)\uff0e\u30a2\u30f3\u30c9\u30ec\u30fb\u30f4\u30a7\u30a4\u30e6\u304c\u5c0e\u5165\u3057\u305f\u306e\u3067\u3042\u308d\u3046\uff0eOno (1957) \u306b\u3088\u308b\u30a2\u30c7\u30fc\u30eb\u7684\u4ee3\u6570\u7fa4\u306e\u4e00\u822c\u7684\u306a\u69cb\u6210\u306f\u30a2\u30eb\u30de\u30f3\u30fb\u30dc\u30ec\u30eb\u3068\u30cf\u30ea\u30b7\u30e5\u30fb\u30c1\u30e3\u30f3\u30c9\u30e9\uff08\u82f1\u8a9e\u7248\uff09\u306b\u3088\u3063\u3066\u57fa\u790e\u3065\u3051\u3089\u308c\u305f\u4ee3\u6570\u7fa4\u306e\u7406\u8ad6\u306b\u7d9a\u3044\u305f\uff0e\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Chevalley, Claude (1936), \u201cG\u00e9n\u00e9ralisation de la th\u00e9orie du corps de classes pour les extensions infinies.\u201d (French), Journal de Math\u00e9matiques Pures et Appliqu\u00e9es 15:  359\u2013371, JFM\u00a062.1153.02\u00a0Chevalley, Claude (1940), \u201cLa th\u00e9orie du corps de classes\u201d, Annals of Mathematics. Second Series 41:  394\u2013418, ISSN\u00a00003-486X, JSTOR\u00a01969013, MR0002357, https:\/\/jstor.org\/stable\/1969013\u00a0Chevalley, Claude (1951), Introduction to the Theory of Algebraic Functions of One Variable, Mathematical Surveys, No. VI, Providence, R.I.: American Mathematical Society, MR0042164\u00a0Jaffard, Paul (1953), Anneaux d’ad\u00e8les (d’apr\u00e8s Iwasawa), S\u00e9minaire Bourbaki,, Secr\u00e9tariat math\u00e9matique, Paris, MR0157859, http:\/\/www.numdam.org\/item?id=SB_1954-1956__3__23_0\u00a0Ono, Takashi (1957), \u201cSur une propri\u00e9t\u00e9 arithm\u00e9tique des groupes alg\u00e9briques commutatifs\u201d, Bulletin de la Soci\u00e9t\u00e9 Math\u00e9matique de France 85:  307\u2013323, ISSN\u00a00037-9484, MR0094362, http:\/\/www.numdam.org\/item?id=BSMF_1957__85__307_0\u00a0Tate, John T. (1950), \u201cFourier analysis in number fields, and Hecke’s zeta-functions\u201d, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., pp.\u00a0305\u2013347, ISBN\u00a0978-0-9502734-2-6, MR0217026\u00a0Weil, Andr\u00e9 (1938), \u201cZur algebraischen Theorie der algebraischen Funktionen.\u201d (German), Journal f\u00fcr Reine und Angewandte Mathematik 179:  129\u2013133, doi:10.1515\/crll.1938.179.129, ISSN\u00a00075-4102, http:\/\/resolver.sub.uni-goettingen.de\/purl?GDZPPN002174502\u00a0\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki21\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/292059#breadcrumbitem","name":"\u30a2\u30c7\u30fc\u30eb\u4ee3\u6570\u7fa4 – Wikipedia"}}]}]