{"title":"互惠剪的加藤复数及其应用","authors":"Sandeep S, Anand Sawant","doi":"arxiv-2403.01735","DOIUrl":null,"url":null,"abstract":"We show that every reciprocity sheaf gives rise to a cycle (pre)module in the\nsense of Rost over a perfect field, under mild additional hypotheses. Over a\nperfect field of positive characteristic, we show that the first cohomology\ngroup of a logarithmic de Rham-Witt sheaf has a partial cycle module structure.\nAs a consequence, we show that Kato complexes of logarithmic de Rham-Witt\nsheaves satisfy functoriality properties similar to Rost's cycle complexes.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"43 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kato complexes of reciprocity sheaves and applications\",\"authors\":\"Sandeep S, Anand Sawant\",\"doi\":\"arxiv-2403.01735\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that every reciprocity sheaf gives rise to a cycle (pre)module in the\\nsense of Rost over a perfect field, under mild additional hypotheses. Over a\\nperfect field of positive characteristic, we show that the first cohomology\\ngroup of a logarithmic de Rham-Witt sheaf has a partial cycle module structure.\\nAs a consequence, we show that Kato complexes of logarithmic de Rham-Witt\\nsheaves satisfy functoriality properties similar to Rost's cycle complexes.\",\"PeriodicalId\":501143,\"journal\":{\"name\":\"arXiv - MATH - K-Theory and Homology\",\"volume\":\"43 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2403.01735\",\"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 - K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.01735","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Kato complexes of reciprocity sheaves and applications
We show that every reciprocity sheaf gives rise to a cycle (pre)module in the
sense of Rost over a perfect field, under mild additional hypotheses. Over a
perfect field of positive characteristic, we show that the first cohomology
group of a logarithmic de Rham-Witt sheaf has a partial cycle module structure.
As a consequence, we show that Kato complexes of logarithmic de Rham-Witt
sheaves satisfy functoriality properties similar to Rost's cycle complexes.