{"id":3717,"date":"2014-06-30T11:43:08","date_gmt":"2014-06-30T11:43:08","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3717"},"modified":"2014-06-30T11:43:08","modified_gmt":"2014-06-30T11:43:08","slug":"lemma-of-the-day-26","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3717","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let X be a quasi-compact and quasi-separated algebraic space. Let T\u2282|X| be a closed subset such that |X| &#8211; T is quasi-compact. The category D_{QCoh,T}(O_X) of complexes with quasi-coherent cohomology sheaves supported on T is generated by a single perfect object. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/0AEC\" title=\"Tag 0AEC\">Lemma Tag 0AEC<\/a><\/p>\n<p>This result for schemes is in the paper &#8220;Dimensions of triangulated categories&#8221; by Rapha\u00ebl Rouquier<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let X be a quasi-compact and quasi-separated algebraic space. Let T\u2282|X| be a closed subset such that |X| &#8211; T is quasi-compact. The category D_{QCoh,T}(O_X) of complexes with quasi-coherent cohomology sheaves supported on T is generated by a single perfect &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3717\">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-3717","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\/3717","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=3717"}],"version-history":[{"count":3,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3717\/revisions"}],"predecessor-version":[{"id":3720,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3717\/revisions\/3720"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3717"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3717"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}