{"id":3748,"date":"2014-07-06T19:42:42","date_gmt":"2014-07-06T19:42:42","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3748"},"modified":"2014-07-06T19:42:42","modified_gmt":"2014-07-06T19:42:42","slug":"lemma-of-the-day-29","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3748","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let X be an algebraic space. Let x \u2208 |X|. If X is separated, locally Noetherian, and the dimension of the local ring of X at x is \u22641 (<a href=\"http:\/\/stacks.math.columbia.edu\/tag\/04NA\" title=\"Tag 04NA\">Definition Tag 04NA<\/a>), then there exists an open subspace of X containing x which is a scheme. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/0ADD\" title=\"Tag 0ADD\">Lemma Tag 0ADD<\/a>.<\/p>\n<p>Slogan: Separated algebraic spaces are schemes in codimension 1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let X be an algebraic space. Let x \u2208 |X|. If X is separated, locally Noetherian, and the dimension of the local ring of X at x is \u22641 (Definition Tag 04NA), then there exists an open subspace of X &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3748\">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-3748","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\/3748","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=3748"}],"version-history":[{"count":1,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3748\/revisions"}],"predecessor-version":[{"id":3749,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3748\/revisions\/3749"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3748"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3748"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}