{"title":"论周氏群伽罗瓦下降的失败","authors":"Humberto A. Diaz","doi":"10.1016/j.jalgebra.2024.11.035","DOIUrl":null,"url":null,"abstract":"<div><div>We show that there are smooth projective surfaces <em>X</em> over a field <em>F</em> for which the cokernel of the extension of scalars map:<span><span><span><math><mi>C</mi><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>→</mo><mspace></mspace><mi>C</mi><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mi>X</mi><msub><mrow><mo>×</mo></mrow><mrow><mi>F</mi></mrow></msub><mover><mrow><mi>F</mi></mrow><mo>‾</mo></mover><mo>)</mo></mrow><mrow><mi>G</mi><mi>a</mi><mi>l</mi><mo>(</mo><mover><mrow><mi>F</mi></mrow><mo>‾</mo></mover><mo>/</mo><mi>F</mi><mo>)</mo></mrow></msup></math></span></span></span> is not of cofinite type.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 203-210"},"PeriodicalIF":0.8000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the failure of Galois descent for Chow groups\",\"authors\":\"Humberto A. Diaz\",\"doi\":\"10.1016/j.jalgebra.2024.11.035\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We show that there are smooth projective surfaces <em>X</em> over a field <em>F</em> for which the cokernel of the extension of scalars map:<span><span><span><math><mi>C</mi><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>→</mo><mspace></mspace><mi>C</mi><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mi>X</mi><msub><mrow><mo>×</mo></mrow><mrow><mi>F</mi></mrow></msub><mover><mrow><mi>F</mi></mrow><mo>‾</mo></mover><mo>)</mo></mrow><mrow><mi>G</mi><mi>a</mi><mi>l</mi><mo>(</mo><mover><mrow><mi>F</mi></mrow><mo>‾</mo></mover><mo>/</mo><mi>F</mi><mo>)</mo></mrow></msup></math></span></span></span> is not of cofinite type.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"667 \",\"pages\":\"Pages 203-210\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324006859\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/3 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324006859","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/3 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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