{"title":"特征 2 中低度卷积的维特不变式","authors":"Jean-Pierre Tignol","doi":"arxiv-2403.15561","DOIUrl":null,"url":null,"abstract":"A $3$-fold and a $5$-fold quadratic Pfister forms are canonically associated\nto every symplectic involution on a central simple algebra of degree $8$ over a\nfield of characteristic $2$. The same construction on central simple algebras\nof degree $4$ associates to every unitary involution a $2$-fold and a $4$-fold\nPfister quadratic forms, and to every orthogonal involution a $1$-fold and a\n$3$-fold quasi-Pfister forms. These forms hold structural information on the\nalgebra with involution.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Invariants de Witt des involutions de bas degré en caractéristique 2\",\"authors\":\"Jean-Pierre Tignol\",\"doi\":\"arxiv-2403.15561\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A $3$-fold and a $5$-fold quadratic Pfister forms are canonically associated\\nto every symplectic involution on a central simple algebra of degree $8$ over a\\nfield of characteristic $2$. The same construction on central simple algebras\\nof degree $4$ associates to every unitary involution a $2$-fold and a $4$-fold\\nPfister quadratic forms, and to every orthogonal involution a $1$-fold and a\\n$3$-fold quasi-Pfister forms. These forms hold structural information on the\\nalgebra with involution.\",\"PeriodicalId\":501143,\"journal\":{\"name\":\"arXiv - MATH - K-Theory and Homology\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2403.15561\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.15561","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Invariants de Witt des involutions de bas degré en caractéristique 2
A $3$-fold and a $5$-fold quadratic Pfister forms are canonically associated
to every symplectic involution on a central simple algebra of degree $8$ over a
field of characteristic $2$. The same construction on central simple algebras
of degree $4$ associates to every unitary involution a $2$-fold and a $4$-fold
Pfister quadratic forms, and to every orthogonal involution a $1$-fold and a
$3$-fold quasi-Pfister forms. These forms hold structural information on the
algebra with involution.