{"title":"正特征全局域上环面复形的对偶性","authors":"C. Demarche, David Harari","doi":"10.5802/jep.129","DOIUrl":null,"url":null,"abstract":"If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When K is a global field of positive characteristic, we prove similar arithmetic duality theorems, including a Poitou-Tate exact sequence for Galois hypercohomology of complexes of tori. One of the main ingredients is Artin-Mazur-Milne duality theorem for fppf cohomology of finite flat commutative group schemes.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"161 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Duality for complexes of tori over a global field of positive characteristic\",\"authors\":\"C. Demarche, David Harari\",\"doi\":\"10.5802/jep.129\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When K is a global field of positive characteristic, we prove similar arithmetic duality theorems, including a Poitou-Tate exact sequence for Galois hypercohomology of complexes of tori. One of the main ingredients is Artin-Mazur-Milne duality theorem for fppf cohomology of finite flat commutative group schemes.\",\"PeriodicalId\":106406,\"journal\":{\"name\":\"Journal de l’École polytechnique — Mathématiques\",\"volume\":\"161 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal de l’École polytechnique — Mathématiques\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/jep.129\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de l’École polytechnique — Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/jep.129","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Duality for complexes of tori over a global field of positive characteristic
If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When K is a global field of positive characteristic, we prove similar arithmetic duality theorems, including a Poitou-Tate exact sequence for Galois hypercohomology of complexes of tori. One of the main ingredients is Artin-Mazur-Milne duality theorem for fppf cohomology of finite flat commutative group schemes.
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