{"id":16436,"date":"2025-03-11T14:38:48","date_gmt":"2025-03-11T13:38:48","guid":{"rendered":"https:\/\/cyberschool.univ-rennes.fr\/?page_id=16436"},"modified":"2026-03-12T14:30:50","modified_gmt":"2026-03-12T13:30:50","slug":"algebre-commutative-et-geometrie-algebrique","status":"publish","type":"page","link":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algebre-commutative-et-geometrie-algebrique\/","title":{"rendered":"Alg\u00e8bre commutative et g\u00e9om\u00e9trie alg\u00e9brique"},"content":{"rendered":"\n<section class=\"txt\">\n    <div class=\"container\">\n        <div class=\"bloc-txt\">\n                            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Course description<\/h2>\n                        <ul>\n<li>Anneaux de polyn\u00f4mes, anneaux factoriels, anneaux locaux, anneaux noeth\u00e9riens, th\u00e9or\u00e8me des z\u00e9ros de Hilbert ;<\/li>\n<li>R\u00e9sultants, bases de Gr\u00f6bner ;<\/li>\n<li>Ensembles alg\u00e9briques affines, topologie de Zariski, ensembles alg\u00e9briques irr\u00e9ductibles, composantes irr\u00e9ductibles ;<\/li>\n<li>Id\u00e9al de d\u00e9finition, anneau de coordonn\u00e9es, fonctions et applications polynomiales, fonctions rationnelles ;<\/li>\n<li>Courbes planes g\u00e9n\u00e9ralis\u00e9es, tangentes, multiplicit\u00e9 d\u2019intersection, th\u00e9or\u00e8me de B\u00e9zout.<\/li>\n<\/ul>\n\n        <\/div>\n    <\/div>\n<\/section>\n\n\n\n<section class=\"txt\">\n    <div class=\"container\">\n        <div class=\"bloc-txt\">\n                            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Biographies<\/h2>\n                        <p><strong>Christophe Mourougane<\/strong> est professeur \u00e0 l\u2019Universit\u00e9 de Rennes.<\/p>\n<p><strong>Tanguy Medevielle<\/strong> est un ancien \u00e9tudiant du master cryptographie. Il pr\u00e9pare actuellement une th\u00e8se \u00e0 l\u2019IRMAR sur les codes alg\u00e9briques sous la direction de Jade Nardi et Sylvain Duquesne.<\/p>\n\n        <\/div>\n    <\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":8,"featured_media":0,"parent":11605,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.13 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Alg\u00e8bre commutative et g\u00e9om\u00e9trie alg\u00e9brique - CyberSchool<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algebre-commutative-et-geometrie-algebrique\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Alg\u00e8bre commutative et g\u00e9om\u00e9trie alg\u00e9brique - 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