{"id":3696,"date":"2014-06-24T11:27:38","date_gmt":"2014-06-24T11:27:38","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3696"},"modified":"2014-06-24T11:27:38","modified_gmt":"2014-06-24T11:27:38","slug":"lemma-of-the-day-21","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3696","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let S be a scheme. Let {X<sub>i<\/sub> &rarr; X}<sub>i &isin; I<\/sub> be an fppf covering of algebraic spaces over S. Assume I is countable (we can allow larger index sets if we bound the size of the algebraic spaces or if we don&#8217;t worry about set theoretic issues). Then any descent datum for algebraic spaces relative to {X<sub>i<\/sub> &rarr; X}<sub>i &isin; I<\/sub> is effective. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/0ADV\" title=\"Tag 0ADV\">Lemma Tag 0ADV<\/a>.<\/p>\n<p>Slogan: fppf descent data for algebraic spaces are effective.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let S be a scheme. Let {Xi &rarr; X}i &isin; I be an fppf covering of algebraic spaces over S. Assume I is countable (we can allow larger index sets if we bound the size of the algebraic spaces or &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3696\">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-3696","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\/3696","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=3696"}],"version-history":[{"count":8,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3696\/revisions"}],"predecessor-version":[{"id":3704,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3696\/revisions\/3704"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3696"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3696"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}