{"id":3941,"date":"2014-10-08T15:21:43","date_gmt":"2014-10-08T15:21:43","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3941"},"modified":"2014-10-08T15:21:43","modified_gmt":"2014-10-08T15:21:43","slug":"spaces-are-fpqc-sheaves","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3941","title":{"rendered":"Spaces are fpqc sheaves"},"content":{"rendered":"<p>Although already mentioned in the <a href=\"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3935\" title=\"Update\">previous post<\/a> I&#8217;d like to point out once again that we have, thanks to Ofer Gabber, now a proof that algebraic spaces satisfy the sheaf condition for fpqc coverings, answering one of the questions in <a href=\"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=855\" title=\"Questions\">this post<\/a>. Also thanks go to Bhargav Bhatt who sent me an email (on 9\/13\/13) explaining Gabber&#8217;s argument. With small comments\/corrections\/clarifications added over the weekend, I hope most of the kinks I introduced have been ironed out.<\/p>\n<p>To read more, start <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/03W8\">here<\/a>. As usual comments and suggestions for improvements are welcome. Enjoy!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Although already mentioned in the previous post I&#8217;d like to point out once again that we have, thanks to Ofer Gabber, now a proof that algebraic spaces satisfy the sheaf condition for fpqc coverings, answering one of the questions in &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3941\">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-3941","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\/3941","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=3941"}],"version-history":[{"count":7,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3941\/revisions"}],"predecessor-version":[{"id":3948,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3941\/revisions\/3948"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3941"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}