{"id":3291,"date":"2013-07-01T12:10:53","date_gmt":"2013-07-01T12:10:53","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3291"},"modified":"2013-07-01T12:10:53","modified_gmt":"2013-07-01T12:10:53","slug":"proposition-of-the-day","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3291","title":{"rendered":"Proposition of the day"},"content":{"rendered":"<p>Let X be a scheme. Let a : X &#8212;> Spec(k<sub>1<\/sub>) and b : X &#8212;> Spec(k<sub>2<\/sub>) be morphisms from X to spectra of fields. Assume a,b are locally of finite type, and X is reduced, and connected. Then we have k\u2032<sub>1<\/sub> = k\u2032<sub>2<\/sub>, where k\u2032<sub>i<\/sub> &sub; \u0393(X,O<sub>X<\/sub>) is the integral closure of k<sub>i<\/sub> in \u0393(X,O<sub>X<\/sub>). See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/04MK\">Tag 04MK<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let X be a scheme. Let a : X &#8212;> Spec(k1) and b : X &#8212;> Spec(k2) be morphisms from X to spectra of fields. Assume a,b are locally of finite type, and X is reduced, and connected. Then we &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3291\">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-3291","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\/3291","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=3291"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3291\/revisions"}],"predecessor-version":[{"id":3314,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3291\/revisions\/3314"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}