{"id":3396,"date":"2013-07-22T15:29:45","date_gmt":"2013-07-22T15:29:45","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3396"},"modified":"2013-07-22T15:29:45","modified_gmt":"2013-07-22T15:29:45","slug":"theorem-of-the-day","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3396","title":{"rendered":"Theorem of the day"},"content":{"rendered":"<p>Let X be an algebraic stack. The following are equivalent<\/p>\n<ol>\n<li>X is DM (see <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/04YW\">Tag 04YW<\/a> and <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/050D\">Tag 050D<\/a>),<\/li>\n<li>X is Deligne-Mumford (see <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/03YO\">Tag 03YO<\/a>), and<\/li>\n<li>there exists a scheme W and a surjective \u00e9tale morphism W\u2192X.<\/li>\n<\/ol>\n<p>See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/06N3\">Tag 06N3<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let X be an algebraic stack. The following are equivalent X is DM (see Tag 04YW and Tag 050D), X is Deligne-Mumford (see Tag 03YO), and there exists a scheme W and a surjective \u00e9tale morphism W\u2192X. See Tag 06N3.<\/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-3396","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\/3396","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=3396"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3396\/revisions"}],"predecessor-version":[{"id":3400,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3396\/revisions\/3400"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}