{"id":3315,"date":"2013-07-03T11:08:03","date_gmt":"2013-07-03T11:08:03","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3315"},"modified":"2013-07-03T11:08:03","modified_gmt":"2013-07-03T11:08:03","slug":"lemma-of-the-day-5","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3315","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let A &#8212;> B be a local homomorphism of Noetherian local rings. Assume A &#8212;> B is formally smooth in the m<sub>B<\/sub>-adic topology. Then A &#8212;> B is flat. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/07NP\">Tag 07NP<\/a>.<\/p>\n<p>PS: Of course much more is true, see <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/07NQ\">Tag 07NQ<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let A &#8212;> B be a local homomorphism of Noetherian local rings. Assume A &#8212;> B is formally smooth in the mB-adic topology. Then A &#8212;> B is flat. See Tag 07NP. PS: Of course much more is true, see &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3315\">Continue reading <span class=\"meta-nav\">&rarr;<\/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-3315","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\/3315","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=3315"}],"version-history":[{"count":5,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3315\/revisions"}],"predecessor-version":[{"id":3322,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3315\/revisions\/3322"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3315"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3315"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}