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Developement of Mathematics Arising from Generalization of Iwasawa Theory

Research Project

Project/Area Number 24654004
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionOsaka University

Principal Investigator

OCHIAI tadashi  大阪大学, 理学(系)研究科(研究院), 准教授 (90372606)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
KeywordsEuler系 / 岩澤理論 / 肥田変形 / Selmer群 / p進L函数 / 岩澤主予想 / Coleman写像 / Coleman family / p進モジュラー形式 / CM体の岩澤主予想 / 肥田理論 / ヒルベルトモジュラー形式
Outline of Final Research Achievements

In this research, we studied mainly (1) behaviour of mixed characteristic complete local rings under specialization (joint with Shimomoto), (2) Iwasawa Main Conjecture for Hilbert modular forms with complex multiplication (joint with Hara), (3) Coleman map for non ordinary Galois deformation (joint with Nuccio). For (1), we finished the first paper and it was recently accepted. We are now preparing the second paper which treats arithmetic applications of the first paper. For (2), we are now in the final revision of the first paper. For (3), we are trying to fill some missing details of the paper and we hope to finish the first paper soon.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (16 results)

All 2015 2014 2013 2012 Other

All Journal Article (3 results) (of which Peer Reviewed: 3 results,  Acknowledgement Compliant: 1 results) Presentation (9 results) (of which Invited: 9 results) Book (1 results) Remarks (3 results)

  • [Journal Article] p-adic L-function and Coleman map for Hida families of GSp_42014

    • Author(s)
      Francesco Lemma, Tadashi Ochiai
    • Journal Title

      American Journal of Mathematics

      Volume: 136 Issue: 3 Pages: 729-760

    • DOI

      10.1353/ajm.2014.0022

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] p-adic L-function and Coleman map for Hida families of GSp_42014

    • Author(s)
      LEMMA, Francesco, OCHIAI, Tadashi
    • Journal Title

      American Journal of Mathematics

      Volume: 136

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Several variables p-adic L-functions for Hida families of Hilbert modular forms2012

    • Author(s)
      Ochiai, Tadashi
    • Journal Title

      Documenta Math.

      Volume: 17

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Some basic problems on critical values and periods of automorphic L-functions in p-adic contexts2015

    • Author(s)
      落合理
    • Organizer
      保型形式の整数論・講演会
    • Place of Presentation
      熊本大学理学部
    • Year and Date
      2015-01-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Remark on the cyclotomic Iwasawa Main Conjecture for ordinary Hilbert cusp forms2014

    • Author(s)
      落合理
    • Organizer
      Automorphic Forms and Arithmetic (a satellite to the ICM, conference number 28)
    • Place of Presentation
      Pohang Mathematics Institute/Korea
    • Year and Date
      2014-08-25
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Coleman map for non-ordinary families of modular Galois representations2014

    • Author(s)
      落合理
    • Organizer
      The sixth annual Pan Asian Number Theory Conference (a satellite to the ICM, conference number 22)
    • Place of Presentation
      Pohang Mathematics Institute/Korea
    • Year and Date
      2014-08-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the Iwasawa Main Conjecture for CM Hilbert cuspforms2014

    • Author(s)
      落合理
    • Organizer
      p-adic aspects of modular forms
    • Place of Presentation
      IISER Pune /India
    • Year and Date
      2014-06-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the cyclotomic Iwasawa Main Conjecture for ordinary Hilbert cusp forms2014

    • Author(s)
      落合理
    • Organizer
      Mini-Workshop on Iwasawa theory
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2014-04-04
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] non-ordinaryなp進モジュラーガロワ表現のColeman写像2014

    • Author(s)
      落合理
    • Organizer
      九州代数的整数論2014 (KANT2014)
    • Place of Presentation
      九州大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Coleman map for families of Galois representations2013

    • Author(s)
      Ochiai, Tadashi
    • Organizer
      Banff Workshop ``Applications of Iwasawa Algebras''
    • Place of Presentation
      Bannff International Research Station/Canada
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Interpolation of dual exponential maps of Bloch-Kato for nearly ordinary deformations2013

    • Author(s)
      Ochiai, Tadashi
    • Organizer
      Number Theory Forum
    • Place of Presentation
      慶応大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Coleman map for families of ordinary Galois representations2012

    • Author(s)
      Ochiai, Tadashi
    • Organizer
      Symposium on ARITHMETIC GEOMETRY
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Book] 岩澤理論とその展望(上)2014

    • Author(s)
      落合理
    • Total Pages
      208
    • Publisher
      岩波書店
    • Related Report
      2014 Annual Research Report
  • [Remarks] 研究活動およびその他の仕事

    • URL

      http://www.math.sci.osaka-u.ac.jp/~ochiai/work.html

    • Related Report
      2014 Annual Research Report
  • [Remarks] 研究活動およびその他の仕事

    • URL

      http://www.math.sci.osaka-u.ac.jp/~ochiai/work.html

    • Related Report
      2013 Research-status Report
  • [Remarks] 研究成果

    • URL

      http://www.math.sci.osaka-u.ac.jp/~ochiai/work.html

    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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