{"id":182040,"date":"2009-04-23T00:00:00","date_gmt":"2009-10-31T09:18:48","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/44-split-jacobians-of-curves-of-genus-2\/"},"modified":"2024-10-01T14:05:17","modified_gmt":"2024-10-01T21:05:17","slug":"44-split-jacobians-of-curves-of-genus-2","status":"publish","type":"msr-video","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/video\/44-split-jacobians-of-curves-of-genus-2\/","title":{"rendered":"(4,4)-split Jacobians of curves of genus 2"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Curves of genus 2 have an associated abelian surface, their jacobian. One can classify genus 2 curves according to special properties of their jacobians. For instance, a jacobian can be split: isogenous to a product of elliptic curves. There are several ways in which jacobians can be split. In this talk we will give a precise description of one of them.<\/p>\n<p>Having such a precise description helps in understanding various number-theoretic and cryptographic constructions.<\/p>\n<p>This is joint work with my student Kevin Doerksen.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Curves of genus 2 have an associated abelian surface, their jacobian. One can classify genus 2 curves according to special properties of their jacobians. For instance, a jacobian can be split: isogenous to a product of elliptic curves. There are several ways in which jacobians can be split. In this talk we will give a [&hellip;]<\/p>\n","protected":false},"featured_media":194424,"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-182040","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\/-74R828paYg","msr_secondary_video_url":"","msr_video_file":"http:\/\/0","_links":{"self":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182040","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":2,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182040\/revisions"}],"predecessor-version":[{"id":1089420,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182040\/revisions\/1089420"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media\/194424"}],"wp:attachment":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media?parent=182040"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=182040"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=182040"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=182040"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=182040"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=182040"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=182040"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=182040"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=182040"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=182040"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}