{"title":"动机同伦理论中的Hurewicz映射","authors":"Utsav Choudhury, A. Hogadi","doi":"10.2140/akt.2022.7.179","DOIUrl":null,"url":null,"abstract":". For an A 1 -connected pointed simplicial sheaf X over a perfect field k , we prove that the Hurewicz map π A 1 1 ( X ) → H A 1 1 ( X ) is surjective. We also observe that the Hurewicz map for P 1 k is the abelianisation map. In the course of proving this result, we also show that for any morphism φ of strongly A 1 -invariant sheaves of groups, the image and kernel of φ are also strongly A 1 -invariant.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"The Hurewicz map in motivic homotopy theory\",\"authors\":\"Utsav Choudhury, A. Hogadi\",\"doi\":\"10.2140/akt.2022.7.179\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". For an A 1 -connected pointed simplicial sheaf X over a perfect field k , we prove that the Hurewicz map π A 1 1 ( X ) → H A 1 1 ( X ) is surjective. We also observe that the Hurewicz map for P 1 k is the abelianisation map. In the course of proving this result, we also show that for any morphism φ of strongly A 1 -invariant sheaves of groups, the image and kernel of φ are also strongly A 1 -invariant.\",\"PeriodicalId\":42182,\"journal\":{\"name\":\"Annals of K-Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/akt.2022.7.179\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/akt.2022.7.179","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
. For an A 1 -connected pointed simplicial sheaf X over a perfect field k , we prove that the Hurewicz map π A 1 1 ( X ) → H A 1 1 ( X ) is surjective. We also observe that the Hurewicz map for P 1 k is the abelianisation map. In the course of proving this result, we also show that for any morphism φ of strongly A 1 -invariant sheaves of groups, the image and kernel of φ are also strongly A 1 -invariant.
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