{"id":550,"date":"2025-01-27T18:09:01","date_gmt":"2025-01-27T17:09:01","guid":{"rendered":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/?page_id=550"},"modified":"2025-08-19T09:11:54","modified_gmt":"2025-08-19T08:11:54","slug":"number-theory-2025-26","status":"publish","type":"page","link":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/number-theory-2025-26\/","title":{"rendered":"Number Theory (2025-26)"},"content":{"rendered":"\n<p>Teachers: Qing Liu and Denis Benois<\/p>\n\n\n\n<p><strong>Program:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dedekind domains and valuations, extensions.<\/li>\n\n\n\n<li>Valued fields. Completion and Hensel&#8217;s lemma.<\/li>\n\n\n\n<li>Ramification theory. Unramified extensions, totally ramified extensions. Tame and wild ramification.<\/li>\n\n\n\n<li>Galois Theory, ramification subgroups.<\/li>\n\n\n\n<li>Some applications in algebraic geometry.<\/li>\n<\/ul>\n\n\n\n<p><strong>Prerequisites:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&nbsp;Theory of Galois extensions of fields;<\/li>\n\n\n\n<li>Basic notion of commutative algebra &nbsp;(modules, localization).<\/li>\n<\/ul>\n\n\n\n<p><strong>Bibliography:<\/strong><\/p>\n\n\n\n<p>F. Lorenz: Algebra II, Universitext (2008), Springer<br>J. Neukirch: Algebraic number theory, GMW 322 (1999), Springer<br>J.-P. Serre: Local fields, GTM 67 (1979), Springer<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Teachers: Qing Liu and Denis Benois Program: Prerequisites: Bibliography: F. Lorenz: Algebra II, Universitext (2008), SpringerJ. Neukirch: Algebraic number theory, GMW 322 (1999), SpringerJ.-P. Serre: Local fields, GTM 67 (1979), Springer<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-550","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/550","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/comments?post=550"}],"version-history":[{"count":3,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/550\/revisions"}],"predecessor-version":[{"id":588,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/550\/revisions\/588"}],"wp:attachment":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/media?parent=550"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}