{"id":548,"date":"2010-06-18T17:31:12","date_gmt":"2010-06-18T17:31:12","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=548"},"modified":"2010-06-18T17:31:12","modified_gmt":"2010-06-18T17:31:12","slug":"update-8","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=548","title":{"rendered":"Update"},"content":{"rendered":"<p>Today I was able to add the result that the quotient stack [U\/R] associated to a smooth groupoid in algebraic spaces is an algebraic stack. See <a href=\"http:\/\/math.columbia.edu\/algebraic_geometry\/stacks-git\/locate.php?tag=04TK\">Theorem Tag 04TK<\/a>.\u00a0Very satisfying!<\/p>\n<p>There are several things that have to be done next:<\/p>\n<ol>\n<li>Work on the chapter Examples of Stacks, and start a parallel chapter Examples of Algebraic Stacks, where we discuss in detail some very basic examples of algebraic stacks.<\/li>\n<li>Add some foundational material on changing the base scheme and the underlying big site. This could then be used to define a 2-category of algebraic stacks which lumps all algebraic stacks together regardless of big site that was used to define them (but I&#8217;m not sure this would be useful, so I may not add this).<\/li>\n<li>Write a Chapter on properties of algebraic stacks<\/li>\n<li>Write a Chapter on morphisms of algebraic stacks<\/li>\n<li>Write about separation axioms for morphisms of algebraic stacks<\/li>\n<li>And so on and so forth.<\/li>\n<\/ol>\n<p>Next week I will not have time to work on the stacks project, so you can start working on the topics above yourself!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Today I was able to add the result that the quotient stack [U\/R] associated to a smooth groupoid in algebraic spaces is an algebraic stack. See Theorem Tag 04TK.\u00a0Very satisfying! There are several things that have to be done next: &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=548\">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-548","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\/548","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=548"}],"version-history":[{"count":5,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/548\/revisions"}],"predecessor-version":[{"id":553,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/548\/revisions\/553"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=548"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=548"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=548"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}