{"@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/1040000781956094464.json","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"17H02836"},{"@type":"JGN","@value":"JP17H02836"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17H02836/"}],"jpcoar:awardTitle":[{"@language":"ja","@value":"代数的サイクルと岩澤理論"},{"@language":"en","@value":"Algebraic cycles and Iwasawa theory"}],"field":[{"keyword":[{"language":"ja","textList":["理工系","数物系科学","数学","代数学"]},{"language":"en","textList":["Science and Engineering","Mathematics and Physics","Mathematics","Algebra"]}]}],"dc:language":"ja","description":[{"type":"outline_of_research_achievement","notation":[{"@language":"ja","@value":"まず一般Heegner cycleと保型形式の反円分岩澤理論について研究し, 非通常素点においても一般Heegner cycleをp進補間するPerrin-Riou理論を構築した. とくにPerrin-Riou twsitの一般化と精密化をおこなった. その後, 大阪大学の太田和惟氏と比較的マイルドな条件の元、この設定における岩澤主予想の半分の不等式を証明した. その後, 太田氏およびカリフォルニア工科大学(現テキサス大学)のAshay Burungale氏と共同で, CM楕円曲線の惰性的素数における反円分岩澤理論の研究を行い, 30年以上未解決であったRubin予想を解決した."},{"@language":"en","@value":"First, we studied generalized Heegner cycles and the anticyclotomic Iwasawa theory of modular forms, and constructed the Perrin-Riou theory interpolating generalized Heegner cycles p-adically even at non-ordinary primes. Especially, we constructed the thery of integral Perrin-Riou twist, which is a generalization and a refinement of the original one. Then, with Kazuto Ota of Osaka University, we proved a half of the inequality of the Iwasawa main conjecture in this setting under relatively mild conditions. Later, in collaboration with Ota and Ashay Burungale of California Institute of Technology (now University of Texas), we studied the anticyclotomic Iwasawa theory of CM elliptic curves at inert primes , and solved the Rubin conjecture, which had been unsolved for more than 30 years."}]},{"type":"significance_of_research_achievement","notation":[{"@language":"ja","@value":"この研究は楕円曲線や保型形式の整数論を拡張し深めるものです. 楕円曲線は1980年頃までは純粋な数学的対象で社会的応用とは無縁でしたが, 今では楕円曲線論を使った暗号理論が構築され, 情報化社会にとって必要不可欠なものになっています. 保型形式も四則演算の次にくる高度な基本演算と位置付けられ, 将来的には社会への応用が見つかると確信しております. (すでに物理学では大きな活躍をしています.) このような数学的に非常に重要な対象の基礎的な研究を, 目先の利益に囚われずロングスパンで行えることこそ, 現在の社会の豊かさの象徴であり, 将来の発展に結びついています."}]}],"researcher":[{"@id":"https://cir.nii.ac.jp/crid/1420282801190510464","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"80362226"},{"@type":"NRID","@value":"1000080362226"},{"@type":"NRID","@value":"9000413564819"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/read0149954"}],"foaf:name":[{"@language":"ja","@value":"小林 真一"},{"@language":"en","@value":"Kobayashi Shinichi"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"九州大学"}],"role":"principal_investigator"},{"@id":"https://cir.nii.ac.jp/crid/1420845751135260032","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"00451518"},{"@type":"NRID","@value":"1000000451518"},{"@type":"NRID","@value":"9000271445354"},{"@type":"NRID","@value":"9000002613314"},{"@type":"NRID","@value":"9000313618518"},{"@type":"NRID","@value":"9000237657160"},{"@type":"NRID","@value":"9000309579858"},{"@type":"NRID","@value":"9000389445481"},{"@type":"NRID","@value":"9000412105570"},{"@type":"NRID","@value":"9000311776784"},{"@type":"NRID","@value":"9000362221583"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/read0138555"}],"foaf:name":[{"@language":"ja","@value":"千田 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