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Yukie Akihiko  雪江 明彦

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YUKIE Akihiko  雪江 明彦

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Researcher Number 20312548
Affiliation (Current) 2025: 東北大学, 理学研究科, 客員研究者
Affiliation (based on the past Project Information) *help 2023: 東北大学, 理学研究科, 客員研究者
2017 – 2022: 京都大学, 理学研究科, 教授
2012 – 2015: 京都大学, 理学(系)研究科(研究院), 教授
2012: 京都大学, 理学研究科, 教授
2011 – 2012: 京都大学, 大学院・理学研究科, 教授 … More
2011: 東北大学, 理学(系)研究科(研究院), 教授
2007 – 2010: 東北大学, 大学院・理学研究科, 教授
2000 – 2005: 東北大学, 大学院・理学研究科, 教授 Less
Review Section/Research Field
Principal Investigator
Algebra / Basic Section 11010:Algebra-related / Algebra
Except Principal Investigator
Algebra / Algebra
Keywords
Principal Investigator
密度定理 / 概均質ベクトル空間 / 代数群 / ゼータ関数 / 有理軌道 / GIT stratification / prehomogeneous / 量子群 / 楕円曲線 / トーリック多様体 … More / 幾何学的不変式論 / automorphic form / invariant theory / algebraic group / density theorem / GIT / 局所密度 / 不変式論 / Frobenius / Motif / Algebraic cycles / Toric Variety / Prehomogeneous vector spaces / 対数的代数幾何 / 密着閉包 / test ideal / 対数アーベル多様体 / フロベニウス写像 / モチーフ / 代数的サイクル / Mordell-Weil group / elliptic curves / tight closure / F-singularities / Q-curves / toric varieties / density theorems / class number / キーワード8 / キーワード7 / キーワード6 / 不定方程式 / 既均質ベクトル空間 / 可積分系 / 密着閉方 / F-特異点 / Q-曲線 / 類数 / 局所ゼータ関数 / 群論 / 数論 / 密度定 / 2次形式 / 整数論 … More
Except Principal Investigator
モティーフ / コホモロジー / 代数的サイクル / 三角圏 / 代数幾何学 / 代数多様体 / cohomology / algebraic cycles / motif / 分解定理 / Representation Theory / Group Theory / Ring Theory / Algebraic Geometry / Number Theory / 解析数論 / 整数論 / 代数学 / 数論的幾何学 / 表現論 / 群論 / 環論 / 代数幾何 / 数論 / チャウ群 / 代数サイクル / Chow群 / モティーフ理論 / 代数多様本 / 特異点 / トーリック / 代数群 / モチーフ / 循環商特異点 / 凸多面体 / 扇 / トーリック多様体 Less
  • Research Projects

    (12 results)
  • Research Products

    (48 results)
  • Co-Researchers

    (22 People)
  •  Number theory of prehomogeneous vector spacesPrincipal Investigator

    • Principal Investigator
      雪江 明彦
    • Project Period (FY)
      2023 – 2025
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 11010:Algebra-related
    • Research Institution
      Tohoku University
  •  Number theory of prehomogeneous vector spacesPrincipal Investigator

    • Principal Investigator
      Yukie Akihiko
    • Project Period (FY)
      2020 – 2023
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 11010:Algebra-related
    • Research Institution
      Tohoku University
      Kyoto University
  •  Number theory of prehomogeneous vector spacesPrincipal Investigator

    • Principal Investigator
      Yukie Akihiko
    • Project Period (FY)
      2017 – 2019
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Kyoto University
  •  Zeta functions pf prehomogeneous vector spacesPrincipal Investigator

    • Principal Investigator
      Yukie Akihiko
    • Project Period (FY)
      2012 – 2015
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Kyoto University
  •  Error terms of density theorems related to prehomogeneous vector spacesPrincipal Investigator

    • Principal Investigator
      YUKIE Akihiko
    • Project Period (FY)
      2011 – 2012
    • Research Category
      Grant-in-Aid for Challenging Exploratory Research
    • Research Field
      Algebra
    • Research Institution
      Kyoto University
      Tohoku University
  •  Mixed motivic sheaves, category theory, and study of cycle complexes

    • Principal Investigator
      HANAMURA Masaki
    • Project Period (FY)
      2009 – 2011
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Tohoku University
  •  Zeta functions of prehomogeneous vector spacesPrincipal Investigator

    • Principal Investigator
      YUKIE Akihiko
    • Project Period (FY)
      2008 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Tohoku University
  •  Extensions and applications of the theory of toric varieties

    • Principal Investigator
      ISHIDA Masanori
    • Project Period (FY)
      2007 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Tohoku University
  •  Number Theory and Geometry related to Algebraic GroupsPrincipal Investigator

    • Principal Investigator
      YUKIE Akihiko
    • Project Period (FY)
      2003 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Tohoku University
  •  Applications of the theory of mixed motifs

    • Principal Investigator
      HANAMURA Masaki
    • Project Period (FY)
      2003 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Tohoku University
  •  Study of relations and applications of Arithmetic Geometry to branches of Algebra

    • Principal Investigator
      MORITA Yasuo
    • Project Period (FY)
      2000 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Tohoku University
  •  Number Theory and Geometry related to Algebraic GroupsPrincipal Investigator

    • Principal Investigator
      YUKIE Akihiko
    • Project Period (FY)
      2000 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Tohoku University

All 2023 2022 2021 2020 2019 2018 2017 2014 2013 2012 2011 2010 2009 2008 2007 2005 2004 Other

All Journal Article Presentation Book

  • [Book] 代数学3代数学の広がり2011

    • Author(s)
      雪江明彦
    • Total Pages
      432
    • Publisher
      日本評論社
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Book] 代数学3代数学のひろがり2011

    • Author(s)
      雪江明彦
    • Total Pages
      432
    • Publisher
      日本評論社
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Book] 代数学1群論入門2010

    • Author(s)
      雪江明彦
    • Total Pages
      158
    • Publisher
      日本評論社
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Book] 代数学2環と体とガロア理論2010

    • Author(s)
      雪江明彦
    • Total Pages
      300
    • Publisher
      日本評論社
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Book] 概説微分積分学2008

    • Author(s)
      雪江明彦
    • Total Pages
      257
    • Publisher
      培風館
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Journal Article] On the density of unnormalized Tamagawa numbers of orthogonal groups III2022

    • Author(s)
      A.Yukie
    • Journal Title

      J. Number Theory

      Volume: 238 Pages: 557-610

    • DOI

      10.1016/j.jnt.2021.09.009

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20K03512
  • [Journal Article] On the GIT stratification of prehomogeneous vector spaces III2022

    • Author(s)
      K.Tajima and A.Yukie
    • Journal Title

      Kyushu J. Math.

      Volume: 76 (2)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20K03512
  • [Journal Article] On the GIT stratification of prehomogeneous vector spaces II2020

    • Author(s)
      K. Tajima and A. Yukie
    • Journal Title

      Tsukuba J. Math.

      Volume: 44 Issue: 1 Pages: 1-62

    • DOI

      10.21099/tkbjm/20204401001

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20K03512
  • [Journal Article] On the density theorem related to the space of non-split tri-{H}ermitian forms II2020

    • Author(s)
      Yukie, Akihiko
    • Journal Title

      Manuscripta Math.

      Volume: 162 Issue: 1-2 Pages: 221-239

    • DOI

      10.1007/s00229-019-01116-x

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05169, KAKENHI-PROJECT-20K03512
  • [Journal Article] Rational orbits of prehomogeneous vector spaces2020

    • Author(s)
      A. Yukie
    • Journal Title

      Algebraic number theory and related topics 2016, RIMS K\^{o}ky\^{u}roku Bessatsu

      Volume: B77 Pages: 179-182

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20K03512
  • [Journal Article] On the GIT stratification of prehomogeneous vector spaces I2020

    • Author(s)
      K. Tajima and A. Yukie
    • Journal Title

      Comment. Math. Univ. St. Pauli

      Volume: 68 Pages: 1-48

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20K03512
  • [Journal Article] On the density theorem related to the space of non-split tri-Hermitian forms I2019

    • Author(s)
      Akihiko Yukie
    • Journal Title

      J. Number Theory

      Volume: 194 Pages: 117-169

    • DOI

      10.1016/j.jnt.2018.07.015

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Journal Article] RATIONAL ORBITS OF PRIMITIVE TRIVECTORS IN DIMENSION SIX2019

    • Author(s)
      Yukie, Akihiko
    • Journal Title

      Tohoku Mathematical Journal, Second Series

      Volume: 71 Issue: 1 Pages: 35-52

    • DOI

      10.2748/tmj/1552100441

    • ISSN
      0040-8735, 2186-585X
    • Year and Date
      2019-03-30
    • Language
      English
    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Journal Article] Rational orbits of prehomogeneous vector spaces2018

    • Author(s)
      A. Yukie
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: to appear

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Journal Article] Rational orbits of the space of pairs of exceptional Jordan algebras2018

    • Author(s)
      Ryo Kato and Akihiko Yukie
    • Journal Title

      J. NUmber Theory

      Volume: 189 Pages: 304-352

    • DOI

      10.1016/j.jnt.2017.12.008

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Journal Article] Rational orbits of primitive trivectors in dimension six2018

    • Author(s)
      A. Yukie
    • Journal Title

      Tohoku Math. J.

      Volume: to appear

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Journal Article] Rational orbits of the space of pairs of exceptional Jordan algebras2018

    • Author(s)
      R. Kato and A. Yukie
    • Journal Title

      J. Number Theory

      Volume: to appear

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Journal Article] Stratification of the null cone in the non-split case2014

    • Author(s)
      Kajima Tajima and Akihiko Yukie
    • Journal Title

      Comment. Math. Univ. St. Pauli

      Volume: 63

    • Peer Reviewed / Acknowledgement Compliant
    • Data Source
      KAKENHI-PROJECT-24340001
  • [Journal Article] On the density of unnormalized Tamagawa numbers of orthogonal groups II2009

    • Author(s)
      N.Hasyasaka, A.Yukie
    • Journal Title

      Amer.J.Math. 131

      Pages: 683-730

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Journal Article] On the density of unnormalized Tamagawa Numbers of orthogonal groups II.2009

    • Author(s)
      N. Hayasaka and A. Yukie
    • Journal Title

      Amer. J. Math

      Volume: 131(3) Pages: 683-730

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Journal Article] On the density of unnormalized Tamagawa numbers of orthogonal groups I2008

    • Author(s)
      N. Hasyasaka and A. Yukie
    • Journal Title

      Publ. Res. Inst. Math. Sci 44

      Pages: 545-607

    • NAID

      110006648231

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Journal Article] On the density of unnormalized Tamagawa Numbers of orthogonal groups I.2008

    • Author(s)
      N. Hayasaka and A. Yukie
    • Journal Title

      Publ. Res. Inst. Math. Sci.

      Volume: 44(2) Pages: 545-608

    • NAID

      110006648231

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Journal Article] On the number of quintic fields.2005

    • Author(s)
      A.C.Kable, A.Yukie
    • Journal Title

      Invent. Math. 160

      Pages: 217-259

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15340001
  • [Journal Article] On the number of quintic fields.2005

    • Author(s)
      A.C.Kable, A.Yukie
    • Journal Title

      Invent.Math. 160

      Pages: 217-259

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15340001
  • [Journal Article] On the space of quadruples of quinary alternating forms2004

    • Author(s)
      A.Kable, A.Yukie
    • Journal Title

      J.Pure Appl.Algebra 186

      Pages: 277-295

    • Data Source
      KAKENHI-PROJECT-15340001
  • [Journal Article] A construction of quintic rings2004

    • Author(s)
      A.Kable, A.Yukie
    • Journal Title

      Nagoya Math.J. 173

      Pages: 163-203

    • Data Source
      KAKENHI-PROJECT-15340001
  • [Journal Article] On a construction of quintic rings2004

    • Author(s)
      A.C.Kable, A.Yukie
    • Journal Title

      Nagoya Math. J. 173

      Pages: 163-203

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15340001
  • [Journal Article] On a construction of quintic rings.2004

    • Author(s)
      A.C.Kable, A.Yukie
    • Journal Title

      Nagoya Math.J. 173

      Pages: 163-203

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15340001
  • [Journal Article] On the number of quintic fields

    • Author(s)
      A.Kable, A.Yukie
    • Journal Title

      Invent.Math. To appear

    • Data Source
      KAKENHI-PROJECT-15340001
  • [Presentation] Rational orbits and density theorems related to prehomogeneous vector spaces2023

    • Author(s)
      Akihiko Yukie
    • Organizer
      代数的整数論とその周辺
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K03512
  • [Presentation] Rational orbits and density theorems related to prehomogeneous vector spaaces2023

    • Author(s)
      Akihiko Yukie
    • Organizer
      代数的整数論とその周辺2023
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-23K03052
  • [Presentation] On the GIT stratification of prehomogeneous vector spaces2021

    • Author(s)
      Akihiko Yukie
    • Organizer
      10th Pan Asian Number Theory Conference.
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K03512
  • [Presentation] On the density theorem related to the space of non-split tri-Hermitian forms2020

    • Author(s)
      Yukie, Akihiko
    • Organizer
      保型形式とL関数の解析的, 幾何的, p進的研究
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Presentation] On the density theorem related to the space of non-split tri-{H}ermitian forms2019

    • Author(s)
      Yukie, Akihiko
    • Organizer
      第6回京都保型形式研究集会
    • Invited
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Presentation] On the local density of prehomoegenous vector spaces2017

    • Author(s)
      A. Yukie
    • Organizer
      4th Kyoto conference on automorphic forms
    • Invited
    • Data Source
      KAKENHI-PROJECT-17K05169
  • [Presentation] On orbits of prehomogeneous vector spaces2014

    • Author(s)
      Akihiko Yukie
    • Organizer
      Prehomogeneous vector spaces and related topics
    • Place of Presentation
      Rikkyo University
    • Year and Date
      2014-09-01
    • Invited
    • Data Source
      KAKENHI-PROJECT-24340001
  • [Presentation] On zeta functions of prehomgenous vector spaces2013

    • Author(s)
      雪江明彦
    • Organizer
      金沢数論ミニ集会2013
    • Place of Presentation
      金沢大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-24340001
  • [Presentation] Prehomogeneous vector spaces and number theory2013

    • Author(s)
      Akihiko Yukie
    • Organizer
      Two-side workshop
    • Place of Presentation
      Tsuinghua University
    • Invited
    • Data Source
      KAKENHI-PROJECT-24340001
  • [Presentation] Jordan分解について2012

    • Author(s)
      雪江明彦
    • Organizer
      第57回代数シンポジウム
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-08-23
    • Data Source
      KAKENHI-PROJECT-24340001
  • [Presentation] On Z_p orbits of prehomogeneous vector spaces2012

    • Author(s)
      雪江明彦
    • Organizer
      Kyoto conference on automorphic forms
    • Place of Presentation
      京都大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-23654003
  • [Presentation] On Z_p orbits of prehomogeneous vector spaces Kyoto conference on automorphic forms2012

    • Author(s)
      雪江明彦
    • Organizer
      Kyoto conference
    • Place of Presentation
      京都大学
    • Data Source
      KAKENHI-PROJECT-23654003
  • [Presentation] Jordan分解について2012

    • Author(s)
      雪江明彦
    • Organizer
      第57回代数シンポジウムKyoto conference on automorphic forms
    • Place of Presentation
      京都大学数理解析研究所
    • Invited
    • Data Source
      KAKENHI-PROJECT-23654003
  • [Presentation] On Z_P orbits of prehomogeneous vector spaces2012

    • Author(s)
      雪江明彦
    • Organizer
      Kyoto conference on automorphic forms
    • Place of Presentation
      京都大学
    • Year and Date
      2012-10-05
    • Data Source
      KAKENHI-PROJECT-24340001
  • [Presentation] Jordan分解について2012

    • Author(s)
      雪江明彦
    • Organizer
      第57回代数シンポジウム
    • Place of Presentation
      数理解析研究所
    • Data Source
      KAKENHI-PROJECT-23654003
  • [Presentation] Prehomogeneous vector spaces and number theory2009

    • Author(s)
      雪江明彦
    • Organizer
      東北復旦代数幾何合同シンポジウム
    • Place of Presentation
      東北大学
    • Year and Date
      2009-11-24
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Presentation] 概均質ベクトル空間と整数論2009

    • Author(s)
      雪江明彦
    • Organizer
      日本数学会代数学賞受賞記念特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Presentation] 概均質ベクトル空間と整数論2008

    • Author(s)
      雪江明彦
    • Organizer
      日本数学会2009年度春季総合分科会代数学賞受賞特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2008-03-28
    • Data Source
      KAKENHI-PROJECT-20540003
  • [Presentation] 代数体上の直交群の非正規玉河数の密度について2007

    • Author(s)
      雪江明彦
    • Organizer
      日本数学会代数分科会一般講演
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-24
    • Data Source
      KAKENHI-PROJECT-19340001
  • 1.  ISHIDA Masanori (30124548)
    # of Collaborated Projects: 6 results
    # of Collaborated Products: 0 results
  • 2.  HANAMURA Masaki (60189587)
    # of Collaborated Projects: 4 results
    # of Collaborated Products: 0 results
  • 3.  OGATA Shoetsu (90177113)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 4.  HARA Nobuo (90298167)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 5.  MORITA Yasuo (20011653)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 6.  KAJIWARA Takeshi (00250663)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 7.  NAKAMURA Tetsuo (90016147)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 8.  ASHIKAGA Tadashi (90125203)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 9.  TSUCHIHASHI Hiroyasu (00146119)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 10.  TAKAHASHI Tomokuni (50259793)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 11.  SATO Hiroshi (20433310)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 12.  KIMURA Shunichi (10284150)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 13.  HIRATA Noriko (90215195)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 14.  SAITO Takeshi (70201506)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 15.  WATANABE Keiichi (10087083)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 16.  伊吹山 知義 (60011722)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 17.  向井 茂 (80115641)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 18.  坂内 英一 (10011652)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 19.  SATO atsushi (30241516)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 20.  長谷川 浩司 (30208483)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 21.  KANEKO Masanobu (70202017)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 22.  SAITO Shuji (50153804)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results

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