"anticyclotomic" meaning in English

See anticyclotomic in All languages combined, or Wiktionary

Adjective

Etymology: anti- + cyclotomic Etymology templates: {{prefix|en|anti|cyclotomic}} anti- + cyclotomic Head templates: {{en-adj|-}} anticyclotomic (not comparable)
  1. (number theory) Pertaining to a Galois character φ, such that φ . (φ ◦ c) = 1, where c is the nontrivial element of Gal(K/Q), where K is an imaginary quadratic field. Tags: not-comparable Categories (topical): Number theory
    Sense id: en-anticyclotomic-en-adj-wyPaEhYI Categories (other): English entries with incorrect language header, English terms prefixed with anti- Topics: mathematics, number-theory, sciences

Download JSON data for anticyclotomic meaning in English (1.7kB)

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "anti",
        "3": "cyclotomic"
      },
      "expansion": "anti- + cyclotomic",
      "name": "prefix"
    }
  ],
  "etymology_text": "anti- + cyclotomic",
  "head_templates": [
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        "1": "-"
      },
      "expansion": "anticyclotomic (not comparable)",
      "name": "en-adj"
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  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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        {
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2015, Santiago Molina Blanco, “Anticyclotomic p-adic l-functions and the exceptional zero phenomenon”, in arXiv",
          "text": "Our methods are based on a new construction of the anticyclotomic p-adic L-function by means of the corresponding automorphic representation..",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Pertaining to a Galois character φ, such that φ . (φ ◦ c) = 1, where c is the nontrivial element of Gal(K/Q), where K is an imaginary quadratic field."
      ],
      "id": "en-anticyclotomic-en-adj-wyPaEhYI",
      "links": [
        [
          "number theory",
          "number theory"
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      ],
      "raw_glosses": [
        "(number theory) Pertaining to a Galois character φ, such that φ . (φ ◦ c) = 1, where c is the nontrivial element of Gal(K/Q), where K is an imaginary quadratic field."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ]
    }
  ],
  "word": "anticyclotomic"
}
{
  "etymology_templates": [
    {
      "args": {
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        "2": "anti",
        "3": "cyclotomic"
      },
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  ],
  "etymology_text": "anti- + cyclotomic",
  "head_templates": [
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  "lang_code": "en",
  "pos": "adj",
  "senses": [
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        "English entries with incorrect language header",
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        "en:Number theory"
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      "examples": [
        {
          "ref": "2015, Santiago Molina Blanco, “Anticyclotomic p-adic l-functions and the exceptional zero phenomenon”, in arXiv",
          "text": "Our methods are based on a new construction of the anticyclotomic p-adic L-function by means of the corresponding automorphic representation..",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Pertaining to a Galois character φ, such that φ . (φ ◦ c) = 1, where c is the nontrivial element of Gal(K/Q), where K is an imaginary quadratic field."
      ],
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          "number theory",
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      "raw_glosses": [
        "(number theory) Pertaining to a Galois character φ, such that φ . (φ ◦ c) = 1, where c is the nontrivial element of Gal(K/Q), where K is an imaginary quadratic field."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "number-theory",
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  ],
  "word": "anticyclotomic"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-20 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.