{"id":3707,"date":"2014-06-26T10:46:56","date_gmt":"2014-06-26T10:46:56","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3707"},"modified":"2014-06-26T10:46:56","modified_gmt":"2014-06-26T10:46:56","slug":"lemma-of-the-day-23","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3707","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let X be a quasi-compact and quasi-separated scheme. Let U, V be quasi-compact disjoint open subschemes of X. Then there exist a (U \u222a V)-admissible blowup b : X\u2032 \u2192 X such that X\u2032 is a disjoint union of open subschemes X\u2032 = X\u20321 \u2a3f X\u20322 with b^{\u22121}(U) \u2282 X\u20321 and b^{\u22121}(V) \u2282 X\u20322. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/080P\" title=\"Tag 080P\">Lemma Tag 080P<\/a>.<\/p>\n<p>Slogan: separate irreducible components by blowing up.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let X be a quasi-compact and quasi-separated scheme. Let U, V be quasi-compact disjoint open subschemes of X. Then there exist a (U \u222a V)-admissible blowup b : X\u2032 \u2192 X such that X\u2032 is a disjoint union of open &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3707\">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-3707","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\/3707","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=3707"}],"version-history":[{"count":1,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3707\/revisions"}],"predecessor-version":[{"id":3708,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3707\/revisions\/3708"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3707"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3707"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}