{"id":3362,"date":"2013-07-16T19:52:24","date_gmt":"2013-07-16T19:52:24","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3362"},"modified":"2013-07-16T19:52:24","modified_gmt":"2013-07-16T19:52:24","slug":"cartier-equality","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3362","title":{"rendered":"Cartier Equality"},"content":{"rendered":"<p>Let K\/k be a finitely generated field extension. Then &Omega;<sub>K\/k<\/sub> and H<sub>1<\/sub>(L<sub>K\/k<\/sub>) are finite dimensional and trdeg<sub>k<\/sub>(K) = dim<sub>K<\/sub> &Omega;<sub>K\/k<\/sub>  &#8211;  dim<sub>K<\/sub> H<sub>1<\/sub>(L<sub>K\/k<\/sub>). See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/07E1\">Tag 07E1<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let K\/k be a finitely generated field extension. Then &Omega;K\/k and H1(LK\/k) are finite dimensional and trdegk(K) = dimK &Omega;K\/k &#8211; dimK H1(LK\/k). See Tag 07E1.<\/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-3362","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\/3362","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=3362"}],"version-history":[{"count":6,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3362\/revisions"}],"predecessor-version":[{"id":3368,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3362\/revisions\/3368"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}