[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2020\/06\/26\/%e3%82%bb%e3%83%bc%e3%83%ab%e5%8f%8c%e5%af%be%e6%80%a7-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2020\/06\/26\/%e3%82%bb%e3%83%bc%e3%83%ab%e5%8f%8c%e5%af%be%e6%80%a7-wikipedia\/","headline":"\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027 – Wikipedia","name":"\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027 – Wikipedia","description":"\u4ee3\u6570\u5e7e\u4f55\u5b66\u3068\u3044\u3046\u6570\u5b66\u306e\u5206\u91ce\u306b\u304a\u3044\u3066\uff0c\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027\uff08\u30bb\u30fc\u30eb\u305d\u3046\u3064\u3044\u305b\u3044\u3001Serre duality\uff09\u306f\uff0c n \u6b21\u5143\u306e\u975e\u7279\u7570\u5c04\u5f71\u4ee3\u6570\u591a\u69d8\u4f53 V\uff08\u3042\u308b\u3044\u306f\u3088\u308a\u4e00\u822c\u7684\u306b\u30d9\u30af\u30c8\u30eb\u675f\u3084\u3055\u3089\u306b\u9023\u63a5\u5c64\uff09\u306b\u95a2\u3059\u308b\u53cc\u5bfe\u6027\u3067\u3042\u308b\uff0e\u305d\u308c\u306f\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4 Hi \u304c\u5225\u306e\u3082\u306e Hn\u2212i \u306e\u53cc\u5bfe\u7a7a\u9593\u3067\u3042\u308b\u8ff0\u3079\u3066\u3044\u308b\uff0e \u6ed1\u3089\u304b\u306a\u30b3\u30f3\u30d1\u30af\u30c8\u8907\u7d20\u591a\u69d8\u4f53 V \u4e0a\u306e\u6b63\u5247\u30d9\u30af\u30c8\u30eb\u675f E \u306b\u5bfe\u3059\u308b\u5834\u5408\u306f\uff0c\u4e3b\u5f35\u306f Hq(V,E)\u2245Hn\u2212q(V,K\u2297E\u2217)\u2217{displaystyle H^{q}(V,E)cong H^{n-q}(V,Kotimes E^{ast })^{ast 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duality\uff09\u306f\uff0c n \u6b21\u5143\u306e\u975e\u7279\u7570\u5c04\u5f71\u4ee3\u6570\u591a\u69d8\u4f53 V\uff08\u3042\u308b\u3044\u306f\u3088\u308a\u4e00\u822c\u7684\u306b\u30d9\u30af\u30c8\u30eb\u675f\u3084\u3055\u3089\u306b\u9023\u63a5\u5c64\uff09\u306b\u95a2\u3059\u308b\u53cc\u5bfe\u6027\u3067\u3042\u308b\uff0e\u305d\u308c\u306f\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4 Hi \u304c\u5225\u306e\u3082\u306e Hn\u2212i \u306e\u53cc\u5bfe\u7a7a\u9593\u3067\u3042\u308b\u8ff0\u3079\u3066\u3044\u308b\uff0e  \u6ed1\u3089\u304b\u306a\u30b3\u30f3\u30d1\u30af\u30c8\u8907\u7d20\u591a\u69d8\u4f53 V \u4e0a\u306e\u6b63\u5247\u30d9\u30af\u30c8\u30eb\u675f E \u306b\u5bfe\u3059\u308b\u5834\u5408\u306f\uff0c\u4e3b\u5f35\u306fHq(V,E)\u2245Hn\u2212q(V,K\u2297E\u2217)\u2217{displaystyle H^{q}(V,E)cong H^{n-q}(V,Kotimes E^{ast })^{ast }}\u3067\u3042\u308a\uff0cV \u306f\u5c04\u5f71\u7684\u3067\u3042\u308b\u5fc5\u8981\u306f\u306a\u3044\uff0e  \u4ee3\u6570\u66f2\u7dda[\u7de8\u96c6]\u4ee3\u6570\u66f2\u7dda\u306e\u5834\u5408\u306f\u65e2\u306b\u30ea\u30fc\u30de\u30f3\u30fb\u30ed\u30c3\u30db\u306e\u5b9a\u7406\u306b\u542b\u307e\u308c\u3066\u3044\u308b\uff0e\u66f2\u7dda C \u306b\u5bfe\u3057\u3066 coherent \u7fa4 Hi \u306f i > 1 \u306b\u5bfe\u3057\u3066\u6d88\u3048\u308b\uff1b\u3057\u304b\u3057 H1 \u306f\u4e00\u822c\u306b\u306f\u975e\u81ea\u660e\u3067\u3042\u308b\uff0e\u5b9f\u969b\uff0c\u5b9a\u7406\u306e\u57fa\u672c\u95a2\u4fc2\u5f0f\u306f l(D) \u3068 l(K \u2212 D) \u306b\u95a2\u308f\u308a\uff0c\u3053\u3053\u3067 D \u306f\u56e0\u5b50\u3067\u3042\u308a K \u306f\u6a19\u6e96\u985e\u306e\u56e0\u5b50\u3067\u3042\u308b\uff0e\u30bb\u30fc\u30eb\u4ee5\u964d\u6211\u3005\u306f l(K \u2212 D) \u3092 H1(D) \u306e\u6b21\u5143\u3068\u8a8d\u8b58\u3057\u3066\u3044\u308b\uff0c\u305f\u3060\u3057\u4eca D \u306f\u56e0\u5b50 D \u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u308b\u76f4\u7dda\u675f\u3092\u610f\u5473\u3059\u308b\uff0e\u3064\u307e\u308a\uff0c\u3053\u306e\u5834\u5408\u306e\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027\u306f\u7fa4 H1(D) \u3068 H0(KD*) \u3092\u95a2\u4fc2\u3065\u3051\uff0c\u6b21\u5143\u306e\u95a2\u4fc2\u304c\u5206\u304b\u308b\uff08\u8868\u8a18\uff1aK \u306f\u6a19\u6e96\u76f4\u7dda\u675f\uff0cD* \u306f\u53cc\u5bfe\u76f4\u7dda\u675f\uff0c\u4e26\u7f6e\u306f\u76f4\u7dda\u675f\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\uff09\uff0e\u3053\u306e\u5b9a\u5f0f\u5316\u306b\u304a\u3044\u3066\uff0c\u30ea\u30fc\u30de\u30f3\u30fb\u30ed\u30c3\u30db\u306e\u5b9a\u7406\u306f\u5c64\u306e\u30aa\u30a4\u30e9\u30fc\u6a19\u6570\uff08\u82f1\u8a9e\u7248\uff09h0(D) \u2212 h1(D),\u3092\u66f2\u7dda\u306e\u7a2e\u6570h1(C,OC),\u3068 D \u306e\u6b21\u6570\u306e\u3053\u3068\u3070\u3067\u8a08\u7b97\u3057\u305f\u3082\u306e\u3068\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u9ad8\u6b21\u5143\u306b\u4e00\u822c\u5316\u3067\u304d\u308b\u306e\u306f\u3053\u306e\u5f62\u3067\u3042\u308b\uff0e  \u3057\u305f\u304c\u3063\u3066\u66f2\u7dda\u306e\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027\u306f\u975e\u5e38\u306b\u53e4\u5178\u7684\u306a\u3082\u306e\u3067\u306f\u3042\u308b\u304c\uff0c\u8208\u5473\u6df1\u3044\u89b3\u70b9\u3092\u6301\u3063\u3066\u3044\u308b\uff0e\u4f8b\u3048\u3070\uff0c\u30ea\u30fc\u30de\u30f3\u9762\u306e\u7406\u8ad6\u306b\u304a\u3044\u3066\uff0c\u8907\u7d20\u69cb\u9020\u306e\u5909\u5f62\u7406\u8ad6\uff08\u82f1\u8a9e\u7248\uff09\u306f\u53e4\u5178\u7684\u306b quadratic differential\uff08\u82f1\u8a9e\u7248\uff09\uff08\u3059\u306a\u308f\u3061 L(K2) \u306e\u5207\u65ad\uff09\u3092\u7528\u3044\u3066\u7814\u7a76\u3055\u308c\u308b\uff0e\u5c0f\u5e73\u90a6\u5f66\u3068 D. C. Spencer\uff08\u82f1\u8a9e\u7248\uff09 \u306e\u5909\u5f62\u7406\u8ad6\u306f H1(T) \u3092\u901a\u3057\u305f\u5909\u5f62\u3092\u540c\u4e00\u8996\u3059\u308b\uff0c\u3053\u3053\u3067 T \u306f\u63a5\u675f\u5c64 K* \u3067\u3042\u308b\uff0e\u53cc\u5bfe\u6027\u306f\u306a\u305c\u3053\u308c\u3089\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u304c\u4e00\u81f4\u3059\u308b\u304b\u3092\u793a\u3059\uff0e\u8d77\u6e90\u3068\u4e00\u822c\u5316[\u7de8\u96c6]\u7406\u8ad6\u306e\u8d77\u6e90\u306f\u591a\u5909\u6570\u8907\u7d20\u95a2\u6570\u8ad6\u306b\u95a2\u3059\u308b\u30bb\u30fc\u30eb\u306e\u5148\u306e\u7814\u7a76\u306b\u3042\u308b\uff0e\u30a2\u30ec\u30af\u30b5\u30f3\u30c9\u30eb\u30fb\u30b0\u30ed\u30bf\u30f3\u30c7\u30a3\u30fc\u30af\u306e\u4e00\u822c\u5316\u306b\u304a\u3044\u3066\uff0c\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027\u306f\u306f\u308b\u304b\u306b\u5e83\u3044\u8a2d\u5b9a\u306b\u304a\u3051\u308b coherent \u53cc\u5bfe\u6027\uff08\u82f1\u8a9e\u7248\uff09\u306e\u4e00\u90e8\u3068\u306a\u308b\uff0eV \u304c\u591a\u69d8\u4f53\u306e\u3068\u304d\u4e0a\u306e K \u306e\u5f79\u5272\u306f\u4e00\u822c\u306e\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027\u3067\u306f\u4f59\u63a5\u675f\u306e\u884c\u5217\u5f0f\u675f\u306b\u3088\u3063\u3066\u306a\u3055\u308c\uff0c\u5b8c\u5168\u306b\u4e00\u822c\u306b\u306f K \u306f V \u306e\u975e\u7279\u7570\u6027\u306e\u306a\u3093\u3089\u304b\u306e\u4eee\u5b9a\u306a\u3057\u3067\u306f\u305f\u30601\u3064\u306e\u5c64\u3067\u306f\u3042\u308a\u3048\u306a\u3044\uff0e\u5b8c\u5168\u306b\u4e00\u822c\u7684\u306a\u5b9a\u5f0f\u5316\u306f\u5c0e\u6765\u570f\u3068 Ext \u95a2\u624b\u3092\u4f7f\u3046\u3053\u3068\u3067\uff0cK \u304c\u5c64\u306e\u9396\u8907\u4f53\uff0c\u3059\u306a\u308f\u3061 dualizing complex\uff08\u82f1\u8a9e\u7248\uff09 \u306b\u3088\u3063\u3066\u8868\u3055\u308c\u308b\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u308b\uff0e\u305d\u308c\u306b\u3082\u304b\u304b\u308f\u3089\u305a\uff0c\u5b9a\u7406\u306e\u4e3b\u5f35\u306f recognisably \u30bb\u30fc\u30eb\u306e\u3082\u306e\u3067\u3042\u308b\uff0e\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u51fa\u5178\u306f\u5217\u6319\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u811a\u6ce8\u306a\u3069\u3092\u7528\u3044\u3066\u3069\u306e\u8a18\u8ff0\u306e\u60c5\u5831\u6e90\u3067\u3042\u308b\u304b\u3092\u660e\u8a18\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u3092\u304a\u9858\u3044\u3044\u305f\u3057\u307e\u3059\u3002\uff082017\u5e748\u6708\uff09Hartshorne, Robin (1977), Algebraic Geometry, Berlin, New York: Springer-Verlag, ISBN\u00a0978-0-387-90244-9, MR0463157, OCLC\u00a013348052\u00a0, see Ch. III.7Hazewinkel, Michiel, ed. (2001), “Duality”, Encyclopaedia of Mathematics, Springer, ISBN\u00a0978-1-55608-010-4\u3002Huybrechts, Daniel (2005), Complex geometry, Berlin: Springer-Verlag\u00a0, see p. 171.Tate, John (1968), \u201cResidues of differentials on curves\u201d, Annales Scientifiques de l’\u00c9cole Normale Sup\u00e9rieure. Quatri\u00e8me S\u00e9rie 1:  149\u2013159, ISSN\u00a00012-9593, http:\/\/archive.numdam.org\/ARCHIVE\/ASENS\/ASENS_1968_4_1_1\/ASENS_1968_4_1_1_149_0\/ASENS_1968_4_1_1_149_0.pdf\u00a0 contains a proof for Serre duality for curvesSerre duality at the weblog Rigorous trivialitiesA link between Poincar\u00e9 and Serre dualities via Hodge theory on Stack exchange"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2020\/06\/26\/%e3%82%bb%e3%83%bc%e3%83%ab%e5%8f%8c%e5%af%be%e6%80%a7-wikipedia\/#breadcrumbitem","name":"\u30bb\u30fc\u30eb\u53cc\u5bfe\u6027 – Wikipedia"}}]}]