{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T07:51:16Z","timestamp":1723276276908},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8320,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:p>Nous consid\u00e9rons des th\u00e9ories d'anneaux locaux reli\u00e9es aux corps <jats:italic>p<\/jats:italic>-adiques, <jats:italic>p<\/jats:italic> un nombre premier. Dans le \u00a71 nous \u00e9tablissons les axiomatisations donn\u00e9es dans [B1], ainsi qu'une autre axiomatisation des anneaux apparaissant dans [R1]. Il s'agit d'anneaux locaux hens\u00e9liens dont le corps r\u00e9siduel est \u00e9l\u00e9mentairement \u00e9quivalent \u00e0 une extension finie d'un corps <jats:italic>p<\/jats:italic>-adique. Nous les appelons anneaux locaux <jats:italic>p<\/jats:italic>-adiquement clos. Dans le contexte de [R1] et [B1] ils apparaissent comme fibres du faisceau structural (aussi appel\u00e9 faisceau de Nash dans [BS]) accompagnant les spectres <jats:italic>p<\/jats:italic>-adiques. L'int\u00e9r\u00eat de nos axiomatisations provient de la simplicit\u00e9 des axiomes qui rendent compte des propri\u00e9t\u00e9s hens\u00e9liennes. Dans le \u00a72 nous donnons une axiomatisation d'une th\u00e9orie d'anneaux locaux qui appara\u00eet naturellement dans le contexte de la th\u00e9orie des mod\u00e8les des corps valu\u00e9s, et se trouve \u00eatre une compl\u00e9tion d'une th\u00e9orie du \u00a71. Nous appelons ces anneaux, anneaux int\u00e8gres <jats:italic>p<\/jats:italic>-adiquement clos.<\/jats:p><jats:p>Dans le \u00a73 nous utilisons \u00a72 pour montrer que les anneaux int\u00e8gres <jats:italic>p<\/jats:italic>-adiquement clos apparaissent aussi comme anneaux quotients d'anneaux de fonctions continues d\u00e9finissables sur les courbes affines <jats:italic>p<\/jats:italic>-adiques. Nous repr\u00e9sentons alors un id\u00e9al premier comme le noyau d'un morphisme d'\u00e9valuation en un point non-standard de la courbe. Le spectre <jats:italic>p<\/jats:italic>-adique fournit un outil commode qui permet de d\u00e9crire la situation de fa\u00e7on concise.<\/jats:p>","DOI":"10.2307\/2274698","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:39:41Z","timestamp":1146940781000},"page":"539-553","source":"Crossref","is-referenced-by-count":5,"title":["Anneaux <i>p<\/i>-adiquement clos et anneaux de fonctions d\u00e9finissables"],"prefix":"10.1017","volume":"56","author":[{"given":"Luc","family":"B\u00e9lair","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200024531_ref022","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(87)90041-X"},{"key":"S0022481200024531_ref023","first-page":"1138","volume":"53","year":"1988","journal-title":"On the structure of semialgebraic sets over p-adic fields"},{"key":"S0022481200024531_ref020","volume-title":"Th\u00e9orie des valuations","year":"1964"},{"key":"S0022481200024531_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389133"},{"key":"S0022481200024531_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/008\/653174"},{"key":"S0022481200024531_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90019-2"},{"key":"S0022481200024531_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(83)90058-0"},{"key":"S0022481200024531_ref004","volume-title":"On the L-adic spectrum","volume":"40","year":"1986"},{"key":"S0022481200024531_ref003","volume-title":"Annales des Sciences Math\u00e9matiques du Qu\u00e9bec"},{"key":"S0022481200024531_ref002","first-page":"151","volume-title":"S\u00e9minaire sur les structures alg\u00e9briques ordonn\u00e9es","volume":"II","year":"1990"},{"key":"S0022481200024531_ref001","first-page":"1","volume":"305","year":"1987","journal-title":"Comptes Rendus des S\u00e9ances de l'Acad\u00e9mie des Sciences, S\u00e9rie 1: Math\u00e9matique"},{"key":"S0022481200024531_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(78)90035-X"},{"key":"S0022481200024531_ref018","volume-title":"Formally p-adic fields","volume":"1050","year":"1984"},{"key":"S0022481200024531_ref017","first-page":"1165","volume":"53","year":"1988","journal-title":"Sheaves of continuous definable functions"},{"key":"S0022481200024531_ref016","first-page":"121","volume-title":"Logic Colloquium '84","year":"1986"},{"key":"S0022481200024531_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(86)90068-X"},{"key":"S0022481200024531_ref014","volume-title":"Stone spaces","year":"1983"},{"key":"S0022481200024531_ref013","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0251026-X"},{"key":"S0022481200024531_ref011","volume-title":"Applications of model theory to real algebraic geometry"},{"key":"S0022481200024531_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/1971463"},{"key":"S0022481200024531_ref026","first-page":"419","volume-title":"Models and sets (Logic Colloquium '83)","volume":"1103","year":"1984"},{"key":"S0022481200024531_ref025","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(81)90339-2"},{"key":"S0022481200024531_ref024","first-page":"97","volume-title":"Logic Colloquium '82","year":"1984"},{"key":"S0022481200024531_ref021","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(86)90047-2"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200024531","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T17:45:34Z","timestamp":1558115134000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200024531\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["S0022481200024531"],"URL":"https:\/\/doi.org\/10.2307\/2274698","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}