Algèbre d'Azumaya

En mathématiques, la notion d'algèbre d'Azumaya est une généralisation de la notion d'algèbre centrale simple aux R-algèbres dont les scalaires R ne forment pas un corps. Elle a été introduite dans un article de Goro Azumaya (en) en 1951, dans le cas où R est un anneau local commutatif, puis a été développée par Alexander Grothendieck comme ingrédient de base à une théorie du groupe de Brauer en géométrie algébrique, dans les séminaires Bourbaki à partir de 1964.

Dans le cas où R est un anneau local, une algèbre d'Azumaya A est une R-algèbre libre et de rang fini r, telle que son produit tensoriel avec son algèbre opposée soit isomorphe à l'algèbre des matrices carrées de taille r sur R.

Du point de vue de la théorie des schémas, Grothendieck la définit comme un faisceau A de OX-algèbres (où X est un schéma, et OX son faisceau structural) localement (pour la topologie étale) isomorphe à un faisceau d'algèbres de matrices. Milne prend en revanche la définition selon laquelle les germes Ax sont des algèbres d'Azumaya sur les anneaux locaux OX,x en tout point x. Le groupe de Brauer est alors défini comme l'ensemble des classes d'équivalence d'algèbres d'Azumaya selon la relation : deux algèbres A1 et A2 sont équivalentes s'il existe des faisceaux localement libres (en) E1 et E2 tels que :

La loi de groupe est obtenue à partir du produit tensoriel, l'élément symétrique étant donné par l'algèbre opposée.

Cette notion a des applications en géométrie arithmétique, notamment grâce au travail de Yuri Manin sur les obstructions au principe de Hasse.


Read other articles:

Disambiguazione – Se stai cercando altri usi dell’espressione, vedi Il falò delle vanità. Questa voce sull'argomento storia medievale è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Bernardino da Siena organizza un falò delle vanità (1457-1461), Agostino di Duccio, Oratorio di San Bernardino, Perugia Il più famoso falò delle vanità avvenne il 7 febbraio 1497 quando in seguito alla cacciata d...

 

 

Amran Syam (25 Mei 1969 – 12 Desember 2020) adalah seorang politikus Indonesia kelahiran Pinrang. Ia lahir dari pasangan Lamasang dan Hanise. Ia menikahi Rahmayani dan memiliki tiga anak, yakni Muhammad Fahrezi Dava Syaputra, Muhammad Fadhlan Khaidir Ramadhan dan Adinda Nabila Putri Syaqila. Ia menjabat sebagai Ketua Dewan Perwakilan Rakyat Daerah (DPRD) Luwu Timur.[1] Ia berasal dari Partai Golkar. Pada pemilihan umum legislatif Indonesia 2019, ia terpilih dengan hasi...

 

 

نظرية المعلومات اعتلاج اعتلاج تفاضلي [الإنجليزية] اعتلاج شرطي اعتلاج مشترك معلومات متبادلة Conditional mutual information تباعد كولباك - ليبلير Entropy rate إسراف Limiting density of discrete points ترميز خاصية تصحيح الخطأ كشف وتصحيح أخطاء Asymptotic equipartition property Rate–distortion theory Shannon's source coding theorem سعة القناة نظرية ت...

American politician John QuitmanMember of the U.S. House of Representativesfrom Mississippi's 5th districtIn officeMarch 4, 1855 – July 17, 1858Preceded byConstituency establishedSucceeded byJohn McRae10th and 16th Governor of MississippiIn officeJanuary 10, 1850 – February 3, 1851Preceded byJoseph W. MatthewsSucceeded byJohn GuionIn officeDecember 3, 1835 – January 7, 1836ActingPreceded byHiram RunnelsSucceeded byCharles Lynch Personal detailsBorn...

 

 

Russian fur cap with ear flaps Sheepskin ushanka winter hat with earflaps An ushanka (Russian: ушанка, Russian pronunciation: [ʊˈʂankə], from уши, 'ears'), also called an ushanka-hat (Russian: шапка-ушанка, romanized: shapka-ushanka, [ˈʂapkə ʊˈʂankə]), is a Russian fur hat with ear-covering flaps that can be tied up on the crown of the cap, or fastened at the chin to protect the ears, jaw, and lower chin from the cold. An alternative way to ...

 

 

Ираклеониты — ученики гностика Ираклеона (II век). Упоминаются как особая секта Епифанием и Августином; при крещении и миропомазании они соблюдали обряд помазания елеем и при этом произносили воззвания на арамейском языке, которые должны были освободить душу от власт�...

British musician (born 1948) Yusuf Islam / Cat StevensStevens performing at Glastonbury Festival 2023Background informationBirth nameSteven Demetre GeorgiouAlso known asSteve AdamsCat StevensYusufBorn (1948-07-21) 21 July 1948 (age 75)London, EnglandGenres Folk rock pop Islamic Occupation(s) Singer-songwriter musician Instrument(s) Vocals guitar keyboards Years active 1965–1980 (as Cat Stevens) 1995–2014 (as Yusuf Islam or Yusuf) 2017–present (as Yusuf / Cat Stevens) Labels Deram I...

 

 

For the British broadcast commentator, see Mike Graham (journalist). Michael GrahamMichael Graham in 2009 giving a speech in downtown BostonBornLos Angeles, CaliforniaAlma materOral Roberts UniversityOccupationRadio hostYears active1998–present Michael Graham (/ɡræm/) is an American conservative media personality and commentator based in Boston. He is a political editor for NH Journal, a columnist for the Boston Herald and a CBS News analyst. Career Graham was born in Los Angele...

 

 

  关于与「內閣總理大臣」標題相近或相同的条目页,請見「內閣總理大臣 (消歧義)」。 日本國內閣總理大臣內閣總理大臣紋章現任岸田文雄自2021年10月4日在任尊称總理、總理大臣、首相、阁下官邸總理大臣官邸提名者國會全體議員選出任命者天皇任期四年,無連任限制[註 1]設立法源日本國憲法先前职位太政大臣(太政官)首任伊藤博文设立1885年12月22日,...

Region of south-central Southern America For the Bolivian province, see Gran Chaco Province. For the Argentine province, see Chaco Province. For the region of Paraguay, see Chaco (Paraguay). This article's lead section may be too short to adequately summarize the key points. Please consider expanding the lead to provide an accessible overview of all important aspects of the article. (May 2020) Gran ChacoDry ChacoLandscape in the Gran Chaco, Chaco Boreal, ParaguayDry Chaco as delimited by the ...

 

 

The UsedInformasi latar belakangAsalOrem, Utah, Amerika SerikatGenrePost hardcore[1] Emo[2] Screamo[3][4]Tahun aktif2001 - sekarangLabelRepriseArtis terkaitStrange Itch Dumb Luck Good Charlotte New Transit Direction RancidSitus webTheUsed.netAnggotaBert McCrackenQuinn AllmanJepha HowardDan WhitesidesMantan anggotaBranden Steineckert Justin Shekoski & Bert McCracken 2015 The Used merupakan sebuah grup musik yang berasal dari Orem, Utah. Anggotanya berjumlah ...

 

 

Uruguay Données clés Surnom Los Teros Données clés Entrée au Board 1989 Sélectionneur Esteban Meneses Record de sélections Diego Magno (104) Record de points Felipe Berchesi (374) Record d’essais Diego Ormaechea (33) Premier match officiel2 juin 1948Chili 21 – 3 UruguayPlus large victoire15 mai 2011Paraguay 6 - 102 UruguayPlus large défaite11 juin 2005Afrique du Sud 134 - 3 Uruguay Données clés Coupe du monde   · Participations 5/10 · Meilleur résultat 3e de p...

Current denomination of New Zealand currency Banknote Twenty dollars(New Zealand)Value20 NZDWidth145 mmHeight70 mmMaterial usedPolymerYears of printing1967–presentObverseDesignElizabeth IIDesign date1992 (original design)May 2016 (current design)ReverseDesignkāreareaDesign date1992 (original design)May 2016 (current design) The New Zealand twenty-dollar note is a New Zealand banknote. It is issued by the Reserve Bank of New Zealand and since 1999 has been a polymer banknote. It w...

 

 

Historical region and former principality in Central and Eastern Europe This article is about the historical principality. For the region of Romania, see Western Moldavia. For the modern state, see Moldova. For other uses, see Moldova (disambiguation). Principality of MoldaviaMoldova, Țara Moldovei (Romanian)1346–1859 Flaga (14th–15th cent.) Coat of armsb(14th–15th cent.) Location of the Principality of Moldavia, 1789Moldavia under Stephen the Great, 1483Status Ottoman vassal[...

 

 

Filipino multinational company This article is about the company. For the fast food chain owned by the company, see Jollibee. Jollibee Foods CorporationCompany typePublicTraded asPSE: JFCISINPHY4466S1007 IndustryRestaurantsFoundedJanuary 11, 1978; 46 years ago (1978-01-11) in Cubao, Quezon City[note 1]FounderTony Tan CaktiongHeadquartersJollibee Plaza, Ortigas Center, Pasig, Metro Manila, PhilippinesNumber of locations 5,933 restaurants (2021)[1]Are...

American jazz guitarist (1943–2017) Larry CoryellCoryell in 1979Background informationBirth nameLorenz Albert Van DeLinder IIIBorn(1943-04-02)April 2, 1943Galveston, Texas, U.S.DiedFebruary 19, 2017(2017-02-19) (aged 73)New York City, U.S.GenresJazz, jazz fusion, free jazz, pop, rock, classicalOccupation(s)MusicianInstrument(s)GuitarYears active1965–2017LabelsVanguard, Arista, Novus, Muse, Shanachie, Chesky, Wide Hive, PatuxentMusical artist Larry Coryell (born Lorenz Albert Van DeLi...

 

 

Casa di Lorenzo BartoliniCasa di Lorenzo BartoliniLocalizzazioneStato Italia RegioneToscana LocalitàFirenze IndirizzoBorgo Pinti 87 Coordinate43°46′34.38″N 11°15′56.32″E43°46′34.38″N, 11°15′56.32″E Informazioni generaliCondizioniIn uso Pianitre Modifica dati su Wikidata · Manuale La casa di Lorenzo Bartolini è un edificio di Firenze situato in Borgo Pinti 87. Qui morì lo scultore nel 1850, come ricorda anche una targa posta sulla facciata. Indice 1 Storia e d...

 

 

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Desember 2022. Patrick Franke (lahir tahun 1967) adalah seorang pakar kajian Islam dari Jerman. Ia menjabat sebagai Profesor Kajian Islam di Universitas Bamberg. Latar belakang Franke mengambil jurusan kajian Islam, hukum, dan kajian Semitik di Universitas Bonn dari...

この記事は検証可能な参考文献や出典が全く示されていないか、不十分です。 出典を追加して記事の信頼性向上にご協力ください。(このテンプレートの使い方)出典検索?: 小山長規 – ニュース · 書籍 · スカラー · CiNii · J-STAGE · NDL · dlib.jp · ジャパンサーチ · TWL (2016年10月) 日本の政治家小山 長規こやま おさのり生年月日 ...

 

 

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Culture of Egypt – news · newspapers · books · scholar · JSTOR (October 2023) (Learn how and when to remove this message)This article is part of a series onLife in Egypt Culture Architecture Ancient Egyptian art Contemporary Cinema Cuisine Dance Belly dance Ra...