{"id":3389,"date":"2013-07-20T13:23:30","date_gmt":"2013-07-20T13:23:30","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3389"},"modified":"2013-07-20T13:23:30","modified_gmt":"2013-07-20T13:23:30","slug":"proposition-of-the-day-4","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3389","title":{"rendered":"Proposition of the day"},"content":{"rendered":"

Let R —> \u039b be a ring map. Let I ⊂ R be an ideal. Assume that<\/p>\n

    \n
  1. I is nilpotent,<\/li>\n
  2. \u039b\/I\u039b is a filtered colimit of smooth R\/I-algebras, and<\/li>\n
  3. R —> \u039b is flat.<\/li>\n<\/ol>\n

    Then \u039b is a colimit of smooth R-algebras. See Tag 07CM<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Let R —> \u039b be a ring map. Let I ⊂ R be an ideal. Assume that I is nilpotent, \u039b\/I\u039b is a filtered colimit of smooth R\/I-algebras, and R —> \u039b is flat. Then \u039b is a colimit of … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3389","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3389"}],"version-history":[{"count":2,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3389\/revisions"}],"predecessor-version":[{"id":3391,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3389\/revisions\/3391"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}