{"id":3692,"date":"2014-06-19T18:25:45","date_gmt":"2014-06-19T18:25:45","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3692"},"modified":"2014-10-20T15:15:23","modified_gmt":"2014-10-20T15:15:23","slug":"example-wanted","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3692","title":{"rendered":"Example wanted"},"content":{"rendered":"<p>Can somebody give me an explicit example of a Noetherian local domain A which does not have resolution of singularities? In particular, I would like an example where the completion A<sup>*<\/sup> of A defines an isolated singularity, i.e., where Spec(A<sup>*<\/sup>) &#8211; {m<sup>*<\/sup>} is a regular scheme?<\/p>\n<p>A related question (I think) is this: Does there exist a Noetherian local ring A such that there exists a proper morphism Y &#8212;> Spec(A<sup>*<\/sup>) whose source Y is an algebraic space which is an isomorphism over the punctured spectrum such that Y is <b>not<\/b> isomorphic to the base change of a proper morphism X &#8212;> Spec(A) whose source is an algebraic space? [<strong>Edit 20 October 2014:<\/strong> This cannot happen; follow link below.]<\/p>\n<p>I wanted to make an example for the second question by taking a Noetherian local ring A which does not have a resolution whose completion A<sup>*<\/sup> is a domain and defines an isolated singularity. Then a resolution of singularities Y of A<sup>*<\/sup> would presumably not be the base change of an X, because if so then X would presumably be a resolution for A. [<strong>Edit 20 October 2014:<\/strong> This cannot happen; follow link below.]<\/p>\n<p>Anyway, I searched for examples of this sort on the web but failed to find a relevant example. Can you help? Thanks!<\/p>\n<p>[<strong>Edit 23 July 2014:<\/strong> The discussion is continued in <a href=\"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3800\">this blog post<\/a>.]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Can somebody give me an explicit example of a Noetherian local domain A which does not have resolution of singularities? In particular, I would like an example where the completion A* of A defines an isolated singularity, i.e., where Spec(A*) &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3692\">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-3692","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\/3692","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=3692"}],"version-history":[{"count":6,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3692\/revisions"}],"predecessor-version":[{"id":3969,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3692\/revisions\/3969"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3692"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3692"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3692"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}