"Langlands conjecture" meaning in English

{
  "etymology_text": "Named after Canadian mathematician Robert Langlands; interpretable as a reference to the Langlands programme.",
  "forms": [
    {
      "form": "Langlands conjectures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Langlands conjecture (plural Langlands conjectures)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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          "source": "w"
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          "name": "Terms with German translations",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1998, Daniel Bump, Automorphic Forms and Representations, Cambridge University Press, page 90:",
          "text": "It^([the Langlands functoriality conjecture]) is closely related to the local Langlands conjectures, which amount to a (conjectural) classification of the representations of reductive groups over local fields.",
          "type": "quote"
        },
        {
          "ref": "2009, Huai-Dong Cao, Shing-Tung Yau, editors, Surveys in Differential Geometry, International Press, page 86:",
          "text": "This abelian case of the Geometric Langlands Conjecture amounts to the well known result that any rank of one local system (or: line bundle with flat connection) on the curve C extends uniquely to J, and this extension is natural with respect to the Abel-Jacobi map.",
          "type": "quote"
        },
        {
          "text": "2013, J. W. Cogdell, 10: Langlands Conjectures for GLₙ, Joseph Bernstein, Stephen Gelbart (editors), An Introduction to the Langlands Program, Springer, page 229,\nThe Langlands conjectures predict the existence of a correspondence between the n-dimensional representations of 𝒢ₖ and the automorphic representations of GLₙ(𝔸) which preserves these analytic invariants."
        }
      ],
      "glosses": [
        "Any of the conjectures that comprise the Langlands programme."
      ],
      "id": "en-Langlands_conjecture-en-noun-vdm2rGh2",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "conjecture",
          "conjecture"
        ],
        [
          "Langlands programme",
          "Langlands programme"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Any of the conjectures that comprise the Langlands programme."
      ],
      "synonyms": [
        {
          "word": "Langlands' conjecture"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "any conjecture of the Langlands programme",
          "tags": [
            "feminine"
          ],
          "word": "Langlands-Vermutung"
        }
      ],
      "wikipedia": [
        "Robert Langlands"
      ]
    }
  ],
  "word": "Langlands conjecture"
}

{
  "etymology_text": "Named after Canadian mathematician Robert Langlands; interpretable as a reference to the Langlands programme.",
  "forms": [
    {
      "form": "Langlands conjectures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "Langlands conjecture (plural Langlands conjectures)",
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    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English countable nouns",
        "English entries with incorrect language header",
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        "English terms with quotations",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with German translations",
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      "examples": [
        {
          "ref": "1998, Daniel Bump, Automorphic Forms and Representations, Cambridge University Press, page 90:",
          "text": "It^([the Langlands functoriality conjecture]) is closely related to the local Langlands conjectures, which amount to a (conjectural) classification of the representations of reductive groups over local fields.",
          "type": "quote"
        },
        {
          "ref": "2009, Huai-Dong Cao, Shing-Tung Yau, editors, Surveys in Differential Geometry, International Press, page 86:",
          "text": "This abelian case of the Geometric Langlands Conjecture amounts to the well known result that any rank of one local system (or: line bundle with flat connection) on the curve C extends uniquely to J, and this extension is natural with respect to the Abel-Jacobi map.",
          "type": "quote"
        },
        {
          "text": "2013, J. W. Cogdell, 10: Langlands Conjectures for GLₙ, Joseph Bernstein, Stephen Gelbart (editors), An Introduction to the Langlands Program, Springer, page 229,\nThe Langlands conjectures predict the existence of a correspondence between the n-dimensional representations of 𝒢ₖ and the automorphic representations of GLₙ(𝔸) which preserves these analytic invariants."
        }
      ],
      "glosses": [
        "Any of the conjectures that comprise the Langlands programme."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "conjecture",
          "conjecture"
        ],
        [
          "Langlands programme",
          "Langlands programme"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Any of the conjectures that comprise the Langlands programme."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Robert Langlands"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "Langlands' conjecture"
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "any conjecture of the Langlands programme",
      "tags": [
        "feminine"
      ],
      "word": "Langlands-Vermutung"
    }
  ],
  "word": "Langlands conjecture"
}