{"id":496,"date":"2024-02-27T15:43:11","date_gmt":"2024-02-27T14:43:11","guid":{"rendered":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/?page_id=496"},"modified":"2025-01-27T17:42:56","modified_gmt":"2025-01-27T16:42:56","slug":"number-theory-24-25","status":"publish","type":"page","link":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/cours\/number-theory-24-25\/","title":{"rendered":"Number Theory (2024-25)"},"content":{"rendered":"\n<p>Teachers: Qing Liu and Pascal Autissier<\/p>\n\n\n\n<p><strong>Program:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>valued fields : absolute values, valuations, complete valued fields, normed vector spaces, extensions of absolute values, Hensel&#8217;s lemma.<\/li>\n\n\n\n<li> ramification : unramified extensions, totally ramified extensions, tame and wild ramification.<\/li>\n\n\n\n<li> local fields : structure of their valuation rings, Witt vectors.<\/li>\n<\/ul>\n\n\n\n<p><strong>Prerequisites:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u00a0Theory of Galois extensions of fields;<\/li>\n\n\n\n<li>Basic notion of commutative algebra \u00a0(modules, localization).<\/li>\n<\/ul>\n\n\n\n<p><strong>Bibliography:<\/strong><\/p>\n\n\n\n<p>P. Samuel:&nbsp;<em>Th\u00e9orie alg\u00e9brique des nombres, Hermann, Paris, 1967<\/em><br>J. Neukirch:&nbsp;<em>Algebraic number theory, GMW 322, Springer, 1999<\/em><br>Z. Borevich, I. Shafarevich:&nbsp;<em>Number theory, Academic Press 1966<\/em><br>J.W.S. Cassels, A. Fr\u00f6hlich (eds):&nbsp;<em>Algebraic number theory, Aca<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Teachers: Qing Liu and Pascal Autissier Program: Prerequisites: Bibliography: P. Samuel:&nbsp;Th\u00e9orie alg\u00e9brique des nombres, Hermann, Paris, 1967J. Neukirch:&nbsp;Algebraic number theory, GMW 322, Springer, 1999Z. Borevich, I. Shafarevich:&nbsp;Number theory, Academic Press 1966J.W.S. Cassels, A. Fr\u00f6hlich (eds):&nbsp;Algebraic number theory, Aca<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":4,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-496","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/496","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=496"}],"version-history":[{"count":4,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/496\/revisions"}],"predecessor-version":[{"id":542,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/496\/revisions\/542"}],"up":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/4"}],"wp:attachment":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/media?parent=496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}