{"id":182200,"date":"2009-01-13T00:00:00","date_gmt":"2009-10-31T09:26:51","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/arithmetic-intersection-and-a-conjecture-of-lauter\/"},"modified":"2018-07-19T08:30:14","modified_gmt":"2018-07-19T15:30:14","slug":"arithmetic-intersection-and-a-conjecture-of-lauter","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/arithmetic-intersection-and-a-conjecture-of-lauter\/","title":{"rendered":"Arithmetic Intersection and a conjecture of Lauter"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Motivated by her joint work with H. Cohn on genus two curve crypotosystem, Lauter gave a very inspiring conjecture on the CM value of Igusa invariants. They need to compute these values to construct `good&#8217; genus two curves. This conjecture led to study of arithmetic intersection on an arithmetic 3-fold (Hilbert modular surface). Recently, I proved an arithmetic intersection formula, which leads to proof of Lauter&#8217;s conjecture. The formula also leads to the first non-abelian generalization of the celebrated Chowla-Selberg formula.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Motivated by her joint work with H. Cohn on genus two curve crypotosystem, Lauter gave a very inspiring conjecture on the CM value of Igusa invariants. They need to compute these values to construct `good&#8217; genus two curves. This conjecture led to study of arithmetic intersection on an arithmetic 3-fold (Hilbert modular surface). Recently, I [&hellip;]<\/p>\n","protected":false},"featured_media":194503,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[13558],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-182200","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/TJeLMyHQyn0","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182200\/revisions"}],"predecessor-version":[{"id":496136,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182200\/revisions\/496136"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/194503"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=182200"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=182200"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=182200"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=182200"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=182200"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=182200"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=182200"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=182200"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=182200"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=182200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}