{"id":3295,"date":"2013-07-04T15:46:11","date_gmt":"2013-07-04T15:46:11","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3295"},"modified":"2013-07-04T15:46:11","modified_gmt":"2013-07-04T15:46:11","slug":"lemma-of-the-day-6","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3295","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let X be a quasi-separated algebraic space. Let E be an object of D<sub>QCoh<\/sub>(O<sub>X<\/sub>). Let a &leq; b. The following are equivalent<\/p>\n<ol>\n<li>E has tor amplitude in [a,b], and<\/li>\n<li>for all F in QCoh(O<sub>X<\/sub>) we have H<sup>i<\/sup>(E &otimes;<sup>L<\/sup> F)=0 for i not in [a,b].<\/li>\n<\/ol>\n<p>See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/08IL\">Tag 08IL<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let X be a quasi-separated algebraic space. Let E be an object of DQCoh(OX). Let a &leq; b. The following are equivalent E has tor amplitude in [a,b], and for all F in QCoh(OX) we have Hi(E &otimes;L F)=0 for &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3295\">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-3295","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\/3295","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=3295"}],"version-history":[{"count":3,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3295\/revisions"}],"predecessor-version":[{"id":3323,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3295\/revisions\/3323"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}