{"title":"高等周氏群的复杂性","authors":"Genival da Silva, James D. Lewis","doi":"10.4153/S0008439522000509","DOIUrl":null,"url":null,"abstract":"Abstract Let \n$X/{\\mathbb C}$\n be a smooth projective variety. We consider two integral invariants, one of which is the level of the Hodge cohomology algebra \n$H^*(X,{\\mathbb C})$\n and the other involving the complexity of the higher Chow groups \n${\\mathrm {CH}}^*(X,m;{\\mathbb Q})$\n for \n$m\\geq 0$\n . We conjecture that these two invariants are the same and accordingly provide some strong evidence in support of this.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The complexity of higher Chow groups\",\"authors\":\"Genival da Silva, James D. Lewis\",\"doi\":\"10.4153/S0008439522000509\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let \\n$X/{\\\\mathbb C}$\\n be a smooth projective variety. We consider two integral invariants, one of which is the level of the Hodge cohomology algebra \\n$H^*(X,{\\\\mathbb C})$\\n and the other involving the complexity of the higher Chow groups \\n${\\\\mathrm {CH}}^*(X,m;{\\\\mathbb Q})$\\n for \\n$m\\\\geq 0$\\n . We conjecture that these two invariants are the same and accordingly provide some strong evidence in support of this.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4153/S0008439522000509\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4153/S0008439522000509","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Abstract Let
$X/{\mathbb C}$
be a smooth projective variety. We consider two integral invariants, one of which is the level of the Hodge cohomology algebra
$H^*(X,{\mathbb C})$
and the other involving the complexity of the higher Chow groups
${\mathrm {CH}}^*(X,m;{\mathbb Q})$
for
$m\geq 0$
. We conjecture that these two invariants are the same and accordingly provide some strong evidence in support of this.