{"id":1603,"date":"2011-06-01T23:35:12","date_gmt":"2011-06-01T23:35:12","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=1603"},"modified":"2011-06-01T23:35:12","modified_gmt":"2011-06-01T23:35:12","slug":"formal-deformation-theory","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=1603","title":{"rendered":"Formal deformation theory"},"content":{"rendered":"<p>Alex Perry wrote a <a href=\"http:\/\/math.columbia.edu\/algebraic_geometry\/stacks-git\/formal-defos.pdf\">chapter on formal deformation theory<\/a> for the stacks project following Schlessinger and Rim. Please read the introduction of that chapter for more information.<\/p>\n<p>I intend to work on this chapter a little bit more in the near future in order to allow for finite residue field extensions (i.e., work with \u039b &#8212;&gt; k of finite type). The way the chapter is written however, I believe only minor changes will have to be made.<\/p>\n<p>Once this is done we intend to use this material to study the formal local structure of algebraic stacks and to explain Artin&#8217;s criteria for Algebraic Stacks. One big obstruction looming in the future is the general Neron desingularization (Popescu). I&#8217;m not yet sure how to deal with this.<\/p>\n<p>More immediately what we really need now is a couple of examples where the theory applies directly as written up. Alex and I listed a few obvious examples at the end of the chapter. If you feel like writing one of these up (should not be more than a few pages) using the framework we have in place please email me (so we don&#8217;t do double work).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alex Perry wrote a chapter on formal deformation theory for the stacks project following Schlessinger and Rim. Please read the introduction of that chapter for more information. I intend to work on this chapter a little bit more in the &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=1603\">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-1603","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\/1603","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=1603"}],"version-history":[{"count":6,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1603\/revisions"}],"predecessor-version":[{"id":1609,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1603\/revisions\/1609"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}