{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1040850857192550656.json","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"21K13774"},{"@type":"JGN","@value":"JP21K13774"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21K13774/"}],"jpcoar:awardTitle":[{"@language":"ja","@value":"保型形式に付随する L 関数の特殊値と数論的不変量のp進的研究"},{"@language":"en","@value":"p-adic analysis of special values of L-values and arithmetic invariants associated to modular forms"}],"field":[{"keyword":[{"language":"ja","textList":["小区分11010:代数学関連"]},{"language":"en","textList":["Basic Section 11010:Algebra-related"]}]}],"dc:language":"ja","description":[{"type":"outline_of_research_initial","notation":[{"@language":"ja","@value":"本研究の目的は、有理数係数の多項式族の零点集合から定義されるような代数多様体に付随する2つの重要な不変量「L 関数の特殊値」と「セルマー群」との神秘的な関係を明らかにすることである。非常に一般的な予想として、Beilinson-Bloch-Kato 予想があるが、一般の状況では未だにほとんど手掛かりがないと言ってよい状況である。したがって、同予想が成り立つ新たな例を見つけることで理解を深めることが重要であると考えられる。本研究では、保型形式とよばれる対象に付随するL関数とセルマー群を研究することで、同予想が成り立つ新たな多様体のクラスを組織的に与えたいと考えている。"}]}],"researcher":[{"@id":"https://cir.nii.ac.jp/crid/1420001326224340608","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"70770775"},{"@type":"NRID","@value":"1000070770775"},{"@type":"NRID","@value":"9000411006348"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/kazutoo"}],"foaf:name":[{"@language":"ja","@value":"太田 和惟"},{"@language":"en","@value":"Ota Kazuto"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"大阪大学"}],"role":"principal_investigator"}],"since":"2021-04-01","until":"2025-03-31","institution":[{"institutionIdentifier":[{"@type":"NII","@value":"0014401"}],"notation":[{"@language":"ja","@value":"大阪大学"},{"@language":"en","@value":"Osaka University"}]}],"fundingProgram":[{"jpcoar:funderName":[{"@language":"ja","@value":"科学研究費助成事業"},{"@language":"en","@value":"Grants-in-Aid for Scientific Research"}]}],"url":[{"@id":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21K13774/","notation":[{"@value":"KAKEN"}]}],"createdAt":"2021-04-28","modifiedAt":"2026-01-16","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=%E5%B2%A9%E6%BE%A4%E7%90%86%E8%AB%96","dc:title":"岩澤理論"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%BB%E3%83%AB%E3%83%9E%E3%83%BC%E6%A7%8B%E9%80%A0","dc:title":"セルマー構造"},{"@id":"https://cir.nii.ac.jp/all?q=CM%E6%A5%95%E5%86%86%E6%9B%B2%E7%B7%9A","dc:title":"CM楕円曲線"},{"@id":"https://cir.nii.ac.jp/all?q=%E5%8F%8D%E5%86%86%E5%88%86%E6%8B%A1%E5%A4%A7","dc:title":"反円分拡大"},{"@id":"https://cir.nii.ac.jp/all?q=Tate-Shafarevich%E7%BE%A4","dc:title":"Tate-Shafarevich群"},{"@id":"https://cir.nii.ac.jp/all?q=L%E9%96%A2%E6%95%B0","dc:title":"L関数"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%BB%E3%83%AB%E3%83%9E%E3%83%BC%E7%BE%A4","dc:title":"セルマー群"},{"@id":"https://cir.nii.ac.jp/all?q=%E4%BF%9D%E5%9E%8B%E5%BD%A2%E5%BC%8F","dc:title":"保型形式"}],"product":[{"@id":"https://cir.nii.ac.jp/crid/1360017280674190976","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.5802/aif.3557"},{"@type":"URI","@value":"https://aif.centre-mersenne.org/item/10.5802/aif.3557.pdf"}],"notation":[{"@value":"On the rank-part of the Mazur–Tate refined conjecture for higher weight modular forms"}]},{"@id":"https://cir.nii.ac.jp/crid/1360013168746053120","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.4007/annals.2021.194.3.8"}],"notation":[{"@value":"Rubin's conjecture on local units in the anticyclotomic tower at inert primes"}]},{"@id":"https://cir.nii.ac.jp/crid/1360302865729878016","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.1007/s40687-023-00387-x"},{"@type":"URI","@value":"https://link.springer.com/content/pdf/10.1007/s40687-023-00387-x.pdf"},{"@type":"URI","@value":"https://link.springer.com/article/10.1007/s40687-023-00387-x/fulltext.html"}],"notation":[{"@value":"On the quantitative variation of congruence ideals and integral periods of modular forms"}]},{"@id":"https://cir.nii.ac.jp/crid/1360302866847558016","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.1017/s147474802300021x"},{"@type":"URI","@value":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S147474802300021X"}],"notation":[{"@value":"<i>p</i>-ADIC <i>L</i>-FUNCTIONS AND RATIONAL POINTS ON CM ELLIPTIC CURVES AT INERT PRIMES"}]},{"@id":"https://cir.nii.ac.jp/crid/1360025431092988160","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.1016/j.jnt.2024.06.014"},{"@type":"URI","@value":"https://api.elsevier.com/content/article/PII:S0022314X24001598?httpAccept=text/xml"},{"@type":"URI","@value":"https://api.elsevier.com/content/article/PII:S0022314X24001598?httpAccept=text/plain"}],"notation":[{"@value":"Kato's epsilon conjecture for anticyclotomic CM deformations at inert primes"}]}],"dataSourceIdentifier":[{"@type":"KAKEN","@value":"21K13774"}],"grant":{"grantIdentifier":[{"@type":"NII","@value":"252"}],"jpcoar:fundingStream":[{"@language":"ja","@value":"若手研究"},{"@language":"en","@value":"Grant-in-Aid for Early-Career Scientists"}]},"allocationClassification":[{"notation":[{"@language":"ja","@value":"基金"},{"@language":"en","@value":"Multi-year Fund"}]}],"projectStatus":"project_closed","allocationAmount":{"totalCost":{"amount":"4550000","currency":"JPY"},"breakdownCost":[{"notation":[{"@language":"ja","@value":"直接経費"},{"@language":"en","@value":"Direct Cost"}],"amount":"3500000","currency":"JPY"},{"notation":[{"@language":"ja","@value":"間接経費"},{"@language":"en","@value":"Indirect Cost"}],"amount":"1050000","currency":"JPY"}]}}