{"title":"Groupes simples résiduellement déployés sur\u0000un corps local","authors":"F. Bruhat, J. Tits","doi":"10.2140/iig.2018.16.209","DOIUrl":"https://doi.org/10.2140/iig.2018.16.209","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124625557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Isotropie des espaces de Klein","authors":"J. Tits","doi":"10.2140/IIG.2018.16.67","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.67","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117030452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"BN-paires de type affine et données\u0000radicielles","authors":"F. Bruhat, J. Tits","doi":"10.2140/IIG.2018.16.203","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.203","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128177250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Espaces et nombres","authors":"J. Tits","doi":"10.2140/IIG.2018.16.287","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.287","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115163709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L'auteur fait le point (en 1970) des connaissances relatives aux homomorphismes et automorphismes des groupes classiques. Il pose le probleme sous une forme tres generale: on a deux corps commutatifs K,K′, un schema en groupes KG[K′G′] sur K[K′], un sous-groupe H[H′] du groupe des points de KG[K′G′] rationnels sur K[K′]. L'auteur decrit d'abord un type d'homomorphisme α:H→H′ qu'il appelle semi-algebrique. On le definit en considerant d'une part un homomorphisme de corps σ:K→K′; si KσG est le schema en groupes sur K′ deduit de KG par le changement de base σ, on a un homomorphisme canonique σ∗ du g certaines conditions, est tel que β(h)=α(h)χ(h), ou α est semi-algebrique et χ un homomorphisme de H dans le centre de H′. Il ne faut s'attendre a une reponse raisonnable que lorsque KG et K′G′ sont des schemas en groupes semi-simples, comme le montrent des exemples pathologiques donnes par l'auteur a la fin de son expose.Les exemples enumeres par l'auteur ou le probleme precedent a une reponse affirmative sont d'une part ceux examines par O'Meara et son ecole par la methode de caracterisation des rotations planes, developpee par O'Meara depuis 1966; d'autre part, ceux qui font l'object des travaux de A. Borel et de l'auteur. Ces derniers s'appliquent a tous les groupes algebriques absolument presque simples (classiques ou "exceptionnels'') pourvuqu'ils soient "isotropes''; par contre cette condition n'intervient pas dans la methode de O'Meara, mais cette derniere est limitee aux groupes classiques.
{"title":"Homomorphismes et automorphismes “abstraits”\u0000de groupes algébriques et arithmétiques","authors":"J. Tits","doi":"10.2140/IIG.2018.16.235","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.235","url":null,"abstract":"L'auteur fait le point (en 1970) des connaissances relatives aux homomorphismes et automorphismes des groupes classiques. Il pose le probleme sous une forme tres generale: on a deux corps commutatifs K,K′, un schema en groupes KG[K′G′] sur K[K′], un sous-groupe H[H′] du groupe des points de KG[K′G′] rationnels sur K[K′]. L'auteur decrit d'abord un type d'homomorphisme α:H→H′ qu'il appelle semi-algebrique. On le definit en considerant d'une part un homomorphisme de corps σ:K→K′; si KσG est le schema en groupes sur K′ deduit de KG par le changement de base σ, on a un homomorphisme canonique σ∗ du g certaines conditions, est tel que β(h)=α(h)χ(h), ou α est semi-algebrique et χ un homomorphisme de H dans le centre de H′. Il ne faut s'attendre a une reponse raisonnable que lorsque KG et K′G′ sont des schemas en groupes semi-simples, comme le montrent des exemples pathologiques donnes par l'auteur a la fin de son expose.Les exemples enumeres par l'auteur ou le probleme precedent a une reponse affirmative sont d'une part ceux examines par O'Meara et son ecole par la methode de caracterisation des rotations planes, developpee par O'Meara depuis 1966; d'autre part, ceux qui font l'object des travaux de A. Borel et de l'auteur. Ces derniers s'appliquent a tous les groupes algebriques absolument presque simples (classiques ou \"exceptionnels'') pourvuqu'ils soient \"isotropes''; par contre cette condition n'intervient pas dans la methode de O'Meara, mais cette derniere est limitee aux groupes classiques.","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"06 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129694297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Notions de géométrie algébrique","authors":"J. Tits, Franz Bingen","doi":"10.2140/IIG.2018.16.301","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.301","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128963972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On “abstract” homomorphisms of simple\u0000algebraic groups","authors":"J. Tits, A. Borel, S. Abhyankar","doi":"10.2140/IIG.2018.16.225","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.225","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126491041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simple groups over local fields","authors":"J. Tits","doi":"10.2140/IIG.2018.16.159","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.159","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115800503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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