{"id":3777,"date":"2014-07-14T01:53:00","date_gmt":"2014-07-14T01:53:00","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3777"},"modified":"2014-07-14T01:53:00","modified_gmt":"2014-07-14T01:53:00","slug":"proposition-of-the-day-5","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3777","title":{"rendered":"Proposition of the day"},"content":{"rendered":"<p>Let A be a ring and let I \u2282 A be a finitely generated ideal. The local cohomology functor and derived completion functor define quasi-inverse equivalences of categories D_{I\u221e-torsion}(A) <---> D_{comp}(A,I). See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/0A6X\">Proposition Tag 0A6X<\/a>.<\/p>\n<p>This and more general statements can be found in <a href=\"http:\/\/stacks.math.columbia.edu\/bibliography\/Dwyer-Greenlees\">Dwyer-Greenlees<\/a>. As usual more references are welcome. Thanks!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let A be a ring and let I \u2282 A be a finitely generated ideal. The local cohomology functor and derived completion functor define quasi-inverse equivalences of categories D_{I\u221e-torsion}(A) D_{comp}(A,I). See Proposition Tag 0A6X. This and more general statements can &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3777\">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-3777","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\/3777","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=3777"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3777\/revisions"}],"predecessor-version":[{"id":3781,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3777\/revisions\/3781"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}