{"title":"群变种扩展的[公式省略]-自洽同调的函数分裂","authors":"","doi":"10.1016/j.indag.2024.05.006","DOIUrl":null,"url":null,"abstract":"<div><div>In this document we consider an exact sequence of group varieties <span><math><mrow><mi>e</mi><mo>→</mo><mi>N</mi><mo>→</mo><mi>G</mi><mo>→</mo><mi>Q</mi><mo>→</mo></mrow></math></span> <span><math><mi>e</mi></math></span> over an algebraically closed field. We show that for <span><math><mrow><mi>l</mi><mo>≠</mo><mi>char</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> a prime there exists an isomorphism of graded <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span>-algebras <span><math><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mover><mrow><mi>e</mi></mrow><mrow><mo>́</mo></mrow></mover><mi>t</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>)</mo></mrow><mo>≅</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mover><mrow><mi>e</mi></mrow><mrow><mo>́</mo></mrow></mover><mi>t</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mrow><mo>(</mo><mi>N</mi><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>)</mo></mrow><msub><mrow><mo>⊗</mo></mrow><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msub><msubsup><mrow><mi>H</mi></mrow><mrow><mover><mrow><mi>e</mi></mrow><mrow><mo>́</mo></mrow></mover><mi>t</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> that is compatible with pullback homomorphisms <span><math><msup><mrow><mi>φ</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> of endomorphisms <span><math><mrow><mi>φ</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>G</mi></mrow></math></span> that stabilize <span><math><mi>N</mi></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 6","pages":"Pages 1185-1196"},"PeriodicalIF":0.5000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Functorial splitting of l-adic cohomology of an extension of group varieties\",\"authors\":\"\",\"doi\":\"10.1016/j.indag.2024.05.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this document we consider an exact sequence of group varieties <span><math><mrow><mi>e</mi><mo>→</mo><mi>N</mi><mo>→</mo><mi>G</mi><mo>→</mo><mi>Q</mi><mo>→</mo></mrow></math></span> <span><math><mi>e</mi></math></span> over an algebraically closed field. We show that for <span><math><mrow><mi>l</mi><mo>≠</mo><mi>char</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> a prime there exists an isomorphism of graded <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span>-algebras <span><math><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mover><mrow><mi>e</mi></mrow><mrow><mo>́</mo></mrow></mover><mi>t</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>)</mo></mrow><mo>≅</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mover><mrow><mi>e</mi></mrow><mrow><mo>́</mo></mrow></mover><mi>t</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mrow><mo>(</mo><mi>N</mi><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>)</mo></mrow><msub><mrow><mo>⊗</mo></mrow><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub></mrow></msub><msubsup><mrow><mi>H</mi></mrow><mrow><mover><mrow><mi>e</mi></mrow><mrow><mo>́</mo></mrow></mover><mi>t</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> that is compatible with pullback homomorphisms <span><math><msup><mrow><mi>φ</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> of endomorphisms <span><math><mrow><mi>φ</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>G</mi></mrow></math></span> that stabilize <span><math><mi>N</mi></math></span>.</div></div>\",\"PeriodicalId\":56126,\"journal\":{\"name\":\"Indagationes Mathematicae-New Series\",\"volume\":\"35 6\",\"pages\":\"Pages 1185-1196\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae-New Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019357724000508\",\"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":"Indagationes Mathematicae-New Series","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019357724000508","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Functorial splitting of l-adic cohomology of an extension of group varieties
In this document we consider an exact sequence of group varieties over an algebraically closed field. We show that for a prime there exists an isomorphism of graded -algebras that is compatible with pullback homomorphisms of endomorphisms that stabilize .
期刊介绍：
Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.
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