{"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":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.5000,"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\":55280,\"journal\":{\"name\":\"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4153/S0008439522000509\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4153/S0008439522000509","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","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.
期刊介绍：
The Canadian Mathematical Bulletin was established in 1958 to publish original, high-quality research papers in all branches of mathematics and to accommodate the growing demand for shorter research papers. The Bulletin is a companion publication to the Canadian Journal of Mathematics that publishes longer papers. New research papers are published continuously online and collated into print issues four times each year.
To be submitted to the Bulletin, papers should be at most 18 pages long and may be written in English or in French. Longer papers should be submitted to the Canadian Journal of Mathematics.
Fondé en 1958, le Bulletin canadien de mathématiques (BCM) publie des articles d’avant-garde et de grande qualité dans toutes les branches des mathématiques, de même que pour répondre à la demande croissante d’articles scientifiques plus brefs. Le BCM se veut une publication complémentaire au Journal canadien de mathématiques, qui publie de longs articles. En ligne, il propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés quatre fois par année.
Les textes présentés au BCM doivent compter au plus 18 pages et être rédigés en anglais ou en français. C’est le Journal canadien de mathématiques qui reçoit les articles plus longs.
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