{"id":3721,"date":"2014-07-01T14:00:44","date_gmt":"2014-07-01T14:00:44","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3721"},"modified":"2014-07-01T14:00:44","modified_gmt":"2014-07-01T14:00:44","slug":"lemma-of-the-day-27","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3721","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let (C,O) be a ringed site. Let (K_n)_{n \u2208 N} be a system of perfect objects of D(O). Let K= hocolim K_n be the derived colimit (<a href=\"http:\/\/stacks.math.columbia.edu\/tag\/090Z\" title=\"Tag 090Z\">Definition Tag 090Z<\/a>). For E in D(O) we have<\/p>\n<blockquote><p>RHom(K, E) = Rlim E &otimes; L_n<\/p><\/blockquote>\n<p>where L_n = RHom(K_n, O) is the inverse system of duals. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/0A0A\" title=\"Tag 0A0A\">Lemma Tag 0A0A<\/a>.<\/p>\n<p>Slogan: Trivial duality for systems of perfect objects.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let (C,O) be a ringed site. Let (K_n)_{n \u2208 N} be a system of perfect objects of D(O). Let K= hocolim K_n be the derived colimit (Definition Tag 090Z). For E in D(O) we have RHom(K, E) = Rlim E &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3721\">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-3721","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\/3721","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=3721"}],"version-history":[{"count":7,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3721\/revisions"}],"predecessor-version":[{"id":3728,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3721\/revisions\/3728"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3721"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3721"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3721"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}