{"id":3448,"date":"2013-07-31T10:55:09","date_gmt":"2013-07-31T10:55:09","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3448"},"modified":"2013-07-31T10:55:09","modified_gmt":"2013-07-31T10:55:09","slug":"lemma-of-the-day-19","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3448","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let S be a scheme. Let Z &sub; S be a closed subscheme. Let b : S\u2032 &#8212;> S be the blowing up of Z in S. Let g : X &#8212;> Y be an affine morphism of schemes over S. Let F be a quasi-coherent sheaf on X. Let g\u2032 : X \u00d7<sub>S<\/sub> S\u2032 &#8212;> Y \u00d7<sub>S<\/sub> S\u2032 be the base change of g. Let F\u2032 be the strict transform of F relative to b. Then g\u2032<sub>\u2217<\/sub>F\u2032 is the strict transform of g<sub>\u2217<\/sub>F. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/080G\">Tag 080G<\/a>.<\/p>\n<p>This tag has one of the densest initial trees in the project:<\/p>\n<p><a href=\"http:\/\/math.columbia.edu\/~dejong\/wordpress\/wp-content\/uploads\/2013\/07\/080G.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/math.columbia.edu\/~dejong\/wordpress\/wp-content\/uploads\/2013\/07\/080G.png\" alt=\"080G\" width=\"1158\" height=\"1066\" class=\"aligncenter size-full wp-image-3449\" srcset=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/wp-content\/uploads\/2013\/07\/080G.png 1158w, https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/wp-content\/uploads\/2013\/07\/080G-300x276.png 300w, https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/wp-content\/uploads\/2013\/07\/080G-1024x942.png 1024w, https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/wp-content\/uploads\/2013\/07\/080G-325x300.png 325w\" sizes=\"auto, (max-width: 1158px) 100vw, 1158px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let S be a scheme. Let Z &sub; S be a closed subscheme. Let b : S\u2032 &#8212;> S be the blowing up of Z in S. Let g : X &#8212;> Y be an affine morphism of schemes over &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3448\">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-3448","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\/3448","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=3448"}],"version-history":[{"count":3,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3448\/revisions"}],"predecessor-version":[{"id":3452,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3448\/revisions\/3452"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3448"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3448"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}