{"title":"相对超 GAGA 定理","authors":"Eita Haibara, Taewan Kim","doi":"arxiv-2409.01481","DOIUrl":null,"url":null,"abstract":"In this paper, we provide relative hypercohomology version of Serre's GAGA\ntheorem. We prove that relative hypercohomology of a complex of sheaves on\ncomplex projective variety with certain conditions and relative hypercohomology\nof its analytification complex are isomorphic. This implies the original\nSerre's GAGA theorem.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Relative-Hyper GAGA Theorem\",\"authors\":\"Eita Haibara, Taewan Kim\",\"doi\":\"arxiv-2409.01481\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we provide relative hypercohomology version of Serre's GAGA\\ntheorem. We prove that relative hypercohomology of a complex of sheaves on\\ncomplex projective variety with certain conditions and relative hypercohomology\\nof its analytification complex are isomorphic. This implies the original\\nSerre's GAGA theorem.\",\"PeriodicalId\":501063,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Geometry\",\"volume\":\"29 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.01481\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.01481","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we provide relative hypercohomology version of Serre's GAGA
theorem. We prove that relative hypercohomology of a complex of sheaves on
complex projective variety with certain conditions and relative hypercohomology
of its analytification complex are isomorphic. This implies the original
Serre's GAGA theorem.
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