{"id":1666,"date":"2011-07-01T14:37:34","date_gmt":"2011-07-01T14:37:34","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=1666"},"modified":"2011-07-01T14:37:34","modified_gmt":"2011-07-01T14:37:34","slug":"update-16","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=1666","title":{"rendered":"Update"},"content":{"rendered":"<p>Just this morning I finished revising the <a href=\"http:\/\/www.math.columbia.edu\/algebraic_geometry\/stacks-git\/formal-defos.pdf\">chapter on formal deformation theory<\/a> that was written by Alex Perry. Next week I hope to put this chapter to use in the stacks project, and start writing about Artin&#8217;s criteria.<\/p>\n<p>In particular, I hope to get back to what I said in <a href=\"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=731\">this post<\/a>. Put in another fashion, I want to prove an equivalence of the form &#8220;Artin&#8217;s criterion holds for stacks in groupoids over S&#8221; <=> &#8220;S is good&#8221; where good is a property of Noetherian base schemes to be determined. Goodness might be closely related to a condition like &#8220;completions of local rings are limits of flat finitely presented algebras&#8221;. I believe this could be fun!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Just this morning I finished revising the chapter on formal deformation theory that was written by Alex Perry. Next week I hope to put this chapter to use in the stacks project, and start writing about Artin&#8217;s criteria. In particular, &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=1666\">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-1666","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\/1666","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=1666"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1666\/revisions"}],"predecessor-version":[{"id":1670,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1666\/revisions\/1670"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}