{"id":488,"date":"2010-06-08T15:06:25","date_gmt":"2010-06-08T15:06:25","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=488"},"modified":"2010-06-08T15:06:25","modified_gmt":"2010-06-08T15:06:25","slug":"proof-of-lemma-tag-03fm","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=488","title":{"rendered":"Proof of Lemma Tag 03FM"},"content":{"rendered":"<p>Finally! The method of proof was discussed in <a href=\"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=110\">this post<\/a>. Actually, the procedure for finding the sub groupoid is better than what I wrote in that blog post, and follows more closely the material in Keel-Mori.<\/p>\n<p>We will soon add another lemma with more hypotheses where the output is a scheme, and not an algebraic space (namely when s, t are separated, locally of finite presentation, and flat). This avoids using Hilbert schemes at the cost of leaving the category of schemes temporarily.<\/p>\n<p>This is a splendid example of an application of the theory of algebraic spaces: Namely, you define some functor, show it is an algebraic space, and then a posteriori you prove it is a scheme by some additional arguments.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Finally! The method of proof was discussed in this post. Actually, the procedure for finding the sub groupoid is better than what I wrote in that blog post, and follows more closely the material in Keel-Mori. We will soon add &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=488\">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-488","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\/488","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=488"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/488\/revisions"}],"predecessor-version":[{"id":492,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/488\/revisions\/492"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=488"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=488"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=488"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}