{"id":3711,"date":"2014-06-28T12:58:39","date_gmt":"2014-06-28T12:58:39","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3711"},"modified":"2014-06-28T12:58:39","modified_gmt":"2014-06-28T12:58:39","slug":"theorem-of-the-day-2","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3711","title":{"rendered":"Theorem of the day"},"content":{"rendered":"<p>Let (A,I) be a henselian pair. Set X = Spec(A) and Z = Spec(A\/I). For any torsion abelian sheaf F on X_{e\u00b4tale} we have H^q_{e\u00b4tale}(X, F) = H^q_{e\u00b4tale}(Z, F|Z). See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/09ZI\" title=\"Tag 09ZI\">Theorem Tag 09ZI<\/a>.<\/p>\n<p>Slogan: Affine analogue of the proper base change theorem (due to Gabber; can also be found in a paper by Huber)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let (A,I) be a henselian pair. Set X = Spec(A) and Z = Spec(A\/I). For any torsion abelian sheaf F on X_{e\u00b4tale} we have H^q_{e\u00b4tale}(X, F) = H^q_{e\u00b4tale}(Z, F|Z). See Theorem Tag 09ZI. Slogan: Affine analogue of the proper base &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3711\">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-3711","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\/3711","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=3711"}],"version-history":[{"count":2,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3711\/revisions"}],"predecessor-version":[{"id":3713,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3711\/revisions\/3713"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3711"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3711"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3711"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}