"Fourier-Mukai transform" meaning in English

See Fourier-Mukai transform in All languages combined, or Wiktionary

Noun

Forms: Fourier-Mukai transforms [plural]
Head templates: {{en-noun}} Fourier-Mukai transform (plural Fourier-Mukai transforms)
  1. (algebraic geometry) A functor Φ_K between derived category of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y).

Inflected forms

{
  "forms": [
    {
      "form": "Fourier-Mukai transforms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Fourier-Mukai transform (plural Fourier-Mukai transforms)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Algebraic geometry",
          "orig": "en:Algebraic geometry",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "A functor Φ_K between derived category of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y)."
      ],
      "id": "en-Fourier-Mukai_transform-en-noun-tAMP~b2N",
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "coherent",
          "coherent"
        ],
        [
          "sheaves",
          "sheaf"
        ],
        [
          "scheme",
          "scheme"
        ],
        [
          "integral transform",
          "integral transform"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) A functor Φ_K between derived category of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y)."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Fourier-Mukai transform"
}
{
  "forms": [
    {
      "form": "Fourier-Mukai transforms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Fourier-Mukai transform (plural Fourier-Mukai transforms)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Algebraic geometry"
      ],
      "glosses": [
        "A functor Φ_K between derived category of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y)."
      ],
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "coherent",
          "coherent"
        ],
        [
          "sheaves",
          "sheaf"
        ],
        [
          "scheme",
          "scheme"
        ],
        [
          "integral transform",
          "integral transform"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) A functor Φ_K between derived category of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y)."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Fourier-Mukai transform"
}

Download raw JSONL data for Fourier-Mukai transform meaning in English (1.2kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-05-08 from the enwiktionary dump dated 2025-05-01 using wiktextract (887c61b and 3d4dee6). 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.