{"id":298,"date":"2019-12-09T10:31:12","date_gmt":"2019-12-09T09:31:12","guid":{"rendered":"https:\/\/web.umons.ac.be\/complexys\/?p=298"},"modified":"2019-12-09T10:34:50","modified_gmt":"2019-12-09T09:34:50","slug":"nathalie-regnault-a-beneficie-dune-bourse-de-6-mois-financee-par-linstitut-complexys-afin-de-terminer-une-these-dans-le-service-de-logique-mathematique-supervisee-par-francoise-poi","status":"publish","type":"post","link":"https:\/\/web.umons.ac.be\/complexys\/fr\/2019\/12\/09\/nathalie-regnault-a-beneficie-dune-bourse-de-6-mois-financee-par-linstitut-complexys-afin-de-terminer-une-these-dans-le-service-de-logique-mathematique-supervisee-par-francoise-poi\/","title":{"rendered":"Nathalie Regnault a b\u00e9n\u00e9fici\u00e9 d\u2019une bourse de 6 mois financ\u00e9e par l\u2019institut Complexys, afin de terminer une th\u00e8se dans le service de logique math\u00e9matique, supervis\u00e9e par Fran\u00e7oise Point et d\u00e9fendue en septembre 2019."},"content":{"rendered":"<blockquote><p><span style=\"color: #333333\">La notion d\u2019alg\u00e9bricit\u00e9 exponentielle a \u00e9t\u00e9 introduite par A.Macintyre<\/span><br \/>\n<span style=\"color: #333333\">dans les ann\u00e9es 80 et est plus complexe que la notion d\u2019alg\u00e9bricit\u00e9. Elle<\/span><br \/>\n<span style=\"color: #333333\">a ensuite \u00e9t\u00e9 caract\u00e9ris\u00e9e par J.Kirby \u00e0 l\u2019aide de d\u00e9rivations exponentielles<\/span><br \/>\n<span style=\"color: #333333\">formelles. On s\u2019appuie sur cette caract\u00e9risation afin d\u2019\u00e9tendre une d\u00e9rivation<\/span><br \/>\n<span style=\"color: #333333\">exponentielle \u00e0 une extension de corps exponentiels. Etant donn\u00e9s un corps<\/span><br \/>\n<span style=\"color: #333333\">exponentiel K et une vari\u00e9t\u00e9 r\u00e9guli\u00e8re V d\u00e9finie sur K en tant qu\u2019ensemble<\/span><br \/>\n<span style=\"color: #333333\">de z\u00e9ros de polyn\u00f4mes exponentiels, on construit une extension \u00e9l\u00e9mentaire<\/span><br \/>\n<span style=\"color: #333333\">L de K, et des points g\u00e9n\u00e9riques de V dans L.<\/span><br \/>\n<span style=\"color: #333333\">Ensuite, partant d\u2019une th\u00e9orie mod\u00e8le-compl\u00e8te de corps exponentiels<\/span><br \/>\n<span style=\"color: #333333\">topologiques dans lesquels on a soit un th\u00e9or\u00e8me des fonctions implicites,<\/span><br \/>\n<span style=\"color: #333333\">soit une propri\u00e9t\u00e9 de largeur, on montre que les expansions diff\u00e9rentielles<\/span><br \/>\n<span style=\"color: #333333\">des mod\u00e8les qui sont existentiellement clos satisfont un sch\u00e9ma de lifting<\/span><br \/>\n<span style=\"color: #333333\">diff\u00e9rentiel. Dans de tels mod\u00e8les le sous-corps des constantes est dense. Ce<\/span><br \/>\n<span style=\"color: #333333\">sch\u00e9ma de lifting diff\u00e9rentiel est dans l\u2019esprit de l\u2019axiomatisation g\u00e9om\u00e9trique<\/span><br \/>\n<span style=\"color: #333333\">des corps de caract\u00e9ristique 0 diff\u00e9rentiellement clos donn\u00e9e par D.Pierce et<\/span><br \/>\n<span style=\"color: #333333\">A.Pillay.<\/span><br \/>\n<span style=\"color: #333333\">A.Wilkie a montr\u00e9 la mod\u00e8le-compl\u00e9tude de la th\u00e9orie du corps ordonn\u00e9<\/span><br \/>\n<span style=\"color: #333333\">des r\u00e9els \u00e9quip\u00e9 de la fonction exponentielle et N.Mariaule la mod\u00e8le-<\/span><br \/>\n<span style=\"color: #333333\">compl\u00e9tude de la th\u00e9orie du corps des nombres complexes p-adiques muni<\/span><br \/>\n<span style=\"color: #333333\">de la fonction exponentielle p-adique sur l\u2019anneau de valuation. Nos r\u00e9sultats<\/span><br \/>\n<span style=\"color: #333333\">s\u2019appliquent aux expansions diff\u00e9rentielles des mod\u00e8les de ces deux th\u00e9ories.<\/span><br \/>\n<span style=\"color: #333333\">Ind\u00e9pendamment, nous montrons des versions des Nullstellens\u00e4tze fort<\/span><br \/>\n<span style=\"color: #333333\">et faible pour les corps exponentiels, ainsi que d\u2019un Nullstellensatz r\u00e9el pour<\/span><br \/>\n<span style=\"color: #333333\">les corps exponentiels partiels ordonn\u00e9s.<\/span><\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Il s\u2019agit d\u2019une th\u00e8se de th\u00e9orie des mod\u00e8les ; on consid\u00e8re des th\u00e9ories de corps exponentiels topologiques de caract\u00e9ristique 0, qui sont \u00e9quip\u00e9s d\u2019une d\u00e9rivation sans interaction avec la topologie.<\/p>\n","protected":false},"author":16,"featured_media":300,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42],"tags":[],"class_list":["post-298","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-recherche"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Nathalie Regnault a b\u00e9n\u00e9fici\u00e9 d\u2019une bourse de 6 mois financ\u00e9e par l\u2019institut Complexys, afin de terminer une th\u00e8se dans le service de logique math\u00e9matique, supervis\u00e9e par Fran\u00e7oise Point et d\u00e9fendue en septembre 2019. - Institut \/ Complexys<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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