{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "FPK5ZH7FKC"
    },
    {
      "field": "specializes",
      "target": "H84VHC8PX2"
    },
    {
      "field": "uses",
      "target": "XWCAS1ESAA"
    }
  ],
  "body": "\n## Summary\n\nAn unramified morphism of schemes is a morphism, locally of finite type, whose fibres are disjoint unions of spectra of finite separable field extensions.\nIt extends to schemes the notion of an unramified extension of number fields.\nAn unramified morphism that is also flat and locally of finite presentation is étale.\n\n## Explanations\n\n### L1 human\n\nA map is unramified when no two sheets of it come together at a point.\nFor the squaring map $t \\mapsto t^2$ on the line, over a field of characteristic not $2$, each nonzero value has two preimages.\nThe value $0$ has only one preimage, where the two sheets touch: the map is ramified there and unramified elsewhere.\nIn number theory, a prime $p$ ramifies in a number field when $p$ has a repeated prime ideal factor in the ring of integers.\nThis is the same phenomenon.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "14A15",
      "14E22"
    ],
    "name": "Unramified morphism",
    "same_as": {
      "wikidata": "Q85812355",
      "wikipedia": "Unramified morphism"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Unramified_morphism"
      }
    ],
    "tag": "1JQX6HD8E5"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/1JQX6HD8E5/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/1JQX6HD8E5.md",
  "msc": [
    "14A15",
    "14E22"
  ],
  "name": "Unramified morphism",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/1JQ/1JQX6HD8E5.md",
  "status": null,
  "tag": "1JQX6HD8E5",
  "uri": "m2://1JQX6HD8E5",
  "url": "https://tamnd.github.io/math2/wiki/unramified-morphism/",
  "writing": {
    "tag": "1JQX6HD8E5",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}