{"title":"Quadratic Riemann-Roch formulas","authors":"Frédéric Déglise, Jean Fasel","doi":"arxiv-2403.09266","DOIUrl":null,"url":null,"abstract":"In this article, we produce Grothendieck-Riemann-Roch formulas for cohomology\ntheories that are not oriented in the classical sense. We then specialize to\nthe case of cohomology theories that admit a so-called symplectic orientation\nand show how to compute the relevant Todd classes in that situation. At the end\nof the article, we illustrate our methods on the Borel character linking\nHermitian K-theory and rational MW-motivic cohomology.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"69 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-14","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-2403.09266","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we produce Grothendieck-Riemann-Roch formulas for cohomology
theories that are not oriented in the classical sense. We then specialize to
the case of cohomology theories that admit a so-called symplectic orientation
and show how to compute the relevant Todd classes in that situation. At the end
of the article, we illustrate our methods on the Borel character linking
Hermitian K-theory and rational MW-motivic cohomology.
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