{"id":3326,"date":"2013-07-07T08:27:38","date_gmt":"2013-07-07T08:27:38","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3326"},"modified":"2013-07-07T08:27:38","modified_gmt":"2013-07-07T08:27:38","slug":"proposition-of-the-day-3","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3326","title":{"rendered":"Proposition of the day"},"content":{"rendered":"<p>Let X be a quasi-compact and separated algebraic space. Let U be an affine scheme, and let f : U &#8212;> X be a surjective \u00e9tale morphism. Let d be an upper bound for the size of the fibres of |U| &#8212;> |X|. Then for any quasi-coherent O<sub>X<\/sub>-module F we have H<sup>q<\/sup>(X,F)=0 for q &ge; d. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/072B\">Tag 072B<\/a>.<\/p>\n<p>Note: This is interesting even when X is a scheme.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let X be a quasi-compact and separated algebraic space. Let U be an affine scheme, and let f : U &#8212;> X be a surjective \u00e9tale morphism. Let d be an upper bound for the size of the fibres of &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3326\">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-3326","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\/3326","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=3326"}],"version-history":[{"count":5,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3326\/revisions"}],"predecessor-version":[{"id":3338,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3326\/revisions\/3338"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}