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Study on triangulated categories and its application to Cohen-Macaulay modules

Research Project

Project/Area Number 21340008
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOkayama University

Principal Investigator

YOSHINO Yuji  岡山大学, 自然科学研究科, 教授 (00135302)

Co-Investigator(Kenkyū-buntansha) ARAYA Tokuji  岡山理科大学, 理学部, 准教授 (70613222)
Co-Investigator(Renkei-kenkyūsha) IYAMA Osamu  名古屋大学, 大学院・多元数理科学研究科, 教授 (70347532)
TAKAHASHI Ryo  名古屋大学, 大学院・多元数理科学研究科, 准教授 (40447719)
YAMAGATA Kunio  東京農工大学, 共生科学技術研究科, 教授 (60015849)
Project Period (FY) 2009-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000)
Fiscal Year 2013: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2010: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Keywords代数学 / 可換環 / Cohen-Macaulay加群 / 導来圏 / 安定圏 / 退化 / Cohen-Macaulay 加群 / 三角圏 / 変形 / 変形と退化
Research Abstract

In order to analyze the degeneration of Cohen-Macaulay modules, we have given careful consideration to the analogue of degeneration in the stable category, which we call the stable degeneration. As a result we obtained several satisfactory results which clarify the degeneration over a simple singularity.
Moreover, about a finitely generated module over a complete local ring of prime characteristic, we gave a proof of the duality theorem between the left Frobenius actions on a module and the right Frobenius actions on its Matlis dual module.

Report

(6 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (59 results)

All 2014 2013 2012 2011 2010 2009 Other

All Journal Article (22 results) (of which Peer Reviewed: 12 results) Presentation (32 results) (of which Invited: 3 results) Remarks (5 results)

  • [Journal Article] Dimensions of triangulated categories with respect to subcategories2014

    • Author(s)
      Aihara, Takuma; Araya, Tokuji; Iyama, Osamu; Takahashi, Ryo; Yoshiwaki,
    • Journal Title

      Journal of Algebra

      Volume: 399

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Examples of degenerations of Cohen-Macaulay modules2013

    • Author(s)
      N. Hiramatsu and Y. Yoshino
    • Journal Title

      Proceedings of the AMS

      Volume: vol. 141

    • Related Report
      2013 Final Research Report
  • [Journal Article] Examples of degenerations of Cohen-Macaulay modules2013

    • Author(s)
      N.Hiramatsu and Y.Yoshino
    • Journal Title

      Proceedings of the American Math. Society

      Volume: 141 Issue: 7 Pages: 2275-2288

    • DOI

      10.1090/s0002-9939-2013-11523-6

    • URL

      http://dx.doi.org/10.1090/S0002-9939-2013-11523-6

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Introduction to representation theory of Cohen-Macaulay modules and their degenerations2012

    • Author(s)
      Yuji Yoshino
    • Journal Title

      Proceedings of the Symposium on Ring Theory and Representation Theory

      Volume: 44 Pages: 268-281

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Stable degenerations of Cohen-Macaulay modules2011

    • Author(s)
      Y. Yoshino
    • Journal Title

      Journal of Algebra

      Volume: vol. 332

    • Related Report
      2013 Final Research Report
  • [Journal Article] Abstract local cohomology functors2011

    • Author(s)
      Y. Yoshino and T. Yoshizawa
    • Journal Title

      Math. Journal of Okayama University

      Volume: vol. 53

    • NAID

      120002693908

    • Related Report
      2013 Final Research Report
  • [Journal Article] Right and left modules over the Frobenius skew polynomial ring in the F-finite case2011

    • Author(s)
      R. Y. Sharp and Y. Yoshino
    • Journal Title

      Mathematical Proceedings of the Cambridge Philosophical Society

      Volume: vol. 150 Pages: 419-438

    • Related Report
      2013 Final Research Report
  • [Journal Article] Right and left modules over the Forbenius skew polynomial ring ring in the F-finite case2011

    • Author(s)
      R.Y.Sharp, Y.Yoshino
    • Journal Title

      Mathematical Proceedings of the Cambridge Philosophical Society

      Volume: 150 Pages: 419-438

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Abstract local cohomology functors2011

    • Author(s)
      Y.Yoshino, T.Yoshizawa
    • Journal Title

      Math.Journal of Okayama University

      Volume: 53 Pages: 129-154

    • NAID

      120002693908

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stable degenerations of Cohen-Macaulay modules2011

    • Author(s)
      Y.Yoshino
    • Journal Title

      Journal of Algebra

      Volume: 332 Pages: 500-521

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On existence of embeddings into modules of finite homological dimensions2010

    • Author(s)
      R. Takahashi, S. Yassemi and Y. Yoshino
    • Journal Title

      Proceedings of the American Math. Soc.

      Volume: vol. 138, no. 7 Pages: 2265-2268

    • NAID

      120007114208

    • Related Report
      2013 Final Research Report
  • [Journal Article] Automorphism groups and Picard groups of additive full subcategories2010

    • Author(s)
      N. Hiramatsu and Y. Yoshino
    • Journal Title

      Mathematica Scandinavica

      Volume: vol. 107 Pages: 5-29

    • Related Report
      2013 Final Research Report
  • [Journal Article] Automorphism groups and Picard groups of additive full subcategories2010

    • Author(s)
      N.Hiramatsu, Y.Yoshino
    • Journal Title

      Mathematica Scandinavica

      Volume: vol.107 Pages: 5-29

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On existence of embeddings into modules of finite homological dimensions2010

    • Author(s)
      R.Takahashi, S.Yassemi, Y.Yoshino
    • Journal Title

      Proceedings of the American Math.Soc.

      Volume: vol.138, no.7 Pages: 2265-2268

    • NAID

      120007114208

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On existence of embeddings into modules of finite homological dimensions2010

    • Author(s)
      R.Takahashi, S.Yassemi, Y.Yoshino
    • Journal Title

      to appear in the Proceedings of the AMS(2010). 138第7号

      Pages: 2265-2268

    • NAID

      120007114208

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Automorphism groups and Picard groups of additive full subcategories2010

    • Author(s)
      N.Hiramatsu, Y.Yoshino
    • Journal Title

      To appear in Math Scandinavica (未定 accept)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Grobner bases for the polynomial ring with infinite variables and their applications2009

    • Author(s)
      K. Iima and Y. Yoshino
    • Journal Title

      Communications in Algebra

      Volume: vol. 37, no. 10 Pages: 3424-3437

    • Related Report
      2013 Final Research Report
  • [Journal Article] On Ext-indices of ring extensions2009

    • Author(s)
      S. Nasseh and Y. Yoshino
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: vol. 213 no. 7 Pages: 1216-1223

    • Related Report
      2013 Final Research Report
  • [Journal Article] Local Cohomology based on a nonclosed support defined by a pair of ideals2009

    • Author(s)
      R. Takahashi, Y. Yoshino and T. Yoshizawa
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: vol. 213 no. 4

    • Related Report
      2013 Final Research Report
  • [Journal Article] Local Cohomology based on a nonclosed support defined by a pair of ideals2009

    • Author(s)
      R.Takahashi, Y.Yoshino, T.Yoshizawa
    • Journal Title

      Journal of Pure and Applied Algebra 213

      Pages: 582-600

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Ext-indices of ring extensions2009

    • Author(s)
      S.Nasseh, Y.Yoshino
    • Journal Title

      Journal of Pure and Applied Algebra 213

      Pages: 1216-1223

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Grobner bases for the Polynomial ring with infinite variables and their applications2009

    • Author(s)
      K.lima, Y.Yoshino
    • Journal Title

      Communications in Algebra 37

      Pages: 3424-3437

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Cohen-Macaulay modules over Cohen-Macaulay rings2014

    • Author(s)
      吉野雄二
    • Organizer
      2014年度代数学賞受賞特別講演
    • Place of Presentation
      日本数学会年会(学習院大学)
    • Year and Date
      2014-03-17
    • Related Report
      2013 Final Research Report
  • [Presentation] Cohen-Macaulay modules over Cohen-Macaulay rings2014

    • Author(s)
      吉野雄二
    • Organizer
      日本数学会2014年度代数学賞受賞特別講演
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A remark on vanishing of chain complexes2013

    • Author(s)
      Yuji Yoshino
    • Organizer
      International conference on commutative algebra and its Interaction to Algebraic Geometry and Combinatorics
    • Place of Presentation
      Hanoi Institute of Math. , Vietnam
    • Year and Date
      2013-12-17
    • Related Report
      2013 Final Research Report
  • [Presentation] Dependence of totally reflexivity conditions2013

    • Author(s)
      Yuji Yoshino
    • Organizer
      Conference honoring Kunio Yamagata on the occasion of his 65th birthday
    • Place of Presentation
      Nagoya University
    • Related Report
      2013 Final Research Report
  • [Presentation] Dependence of totally reflexivity conditions2013

    • Author(s)
      Yuji Yoshino
    • Organizer
      Perspectives of Representation Theory of Algebras
    • Place of Presentation
      名古屋大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A remark on vanishing of chain complexes2013

    • Author(s)
      Yuji Yoshino
    • Organizer
      International conference on commutative algebra and its Interaction to Algebraic Geometry and Combinatorics
    • Place of Presentation
      Hanoins Institute of Math., Vietnam
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 行列分解と超曲面上のコーエン・マコーレー加群について2013

    • Author(s)
      荒谷督司
    • Organizer
      代数学シンポジウム
    • Place of Presentation
      広島大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Thick subcategories of stable categories over graded Gorenstein rings2013

    • Author(s)
      荒谷督司
    • Organizer
      第35回 可換環論シンポジウム
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] Universal deformations of modules along non-commutative parameters2012

    • Author(s)
      Yuji Yoshino
    • Organizer
      Colloquium Talk at Nebraska University
    • Place of Presentation
      Lincoln
    • Year and Date
      2012-02-10
    • Related Report
      2013 Final Research Report
  • [Presentation] Universal deformations of modules along non-commutative parameters2012

    • Author(s)
      Yuji Yoshino
    • Organizer
      Colloquium at Nebraska University, Lincoln
    • Place of Presentation
      Nebraska University, Lincoln, the USA
    • Year and Date
      2012-02-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] Deformations and degenerations of modules2012

    • Author(s)
      Yuji Yoshino
    • Organizer
      Seminar Talk at Nebraska University
    • Place of Presentation
      Lincoln
    • Year and Date
      2012-02-09
    • Related Report
      2013 Final Research Report
  • [Presentation] Primary decompositions in abelian categories2011

    • Author(s)
      Yuji Yoshino
    • Organizer
      The 7th Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      Quy Nhon University, Vietnam
    • Related Report
      2013 Final Research Report
  • [Presentation] Introduction of representation theory of Cohen-Macaulay modules and their degenerations I,II2011

    • Author(s)
      吉野雄二
    • Organizer
      第44回環論および表現論シンポジウム
    • Place of Presentation
      岡山大学理学部
    • Related Report
      2013 Final Research Report
  • [Presentation] Degeneration and stable degeneration of Cohen-Macaulay modules2011

    • Author(s)
      Yuji Yoshino
    • Organizer
      Joint CIMPA-ICTP-UNESCO-MICINN-INDONESIA Research School
    • Place of Presentation
      Institut Teknologi Bandung, Indonesia
    • Related Report
      2013 Final Research Report
  • [Presentation] Degeneration and stable degeneration of Cohen-Macaulay modules2011

    • Author(s)
      Yuji Yoshino
    • Organizer
      Joint CIMPA-ICTP-UNESCO-MICINN-INDONESI A Research School
    • Place of Presentation
      Institut Teknologi Bandung, Indonesia(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Introduction of representation theory of Cohen-Macaulay modules and their degenerations I, IT2011

    • Author(s)
      吉野雄二
    • Organizer
      第44回環論および表現論シンポジウム
    • Place of Presentation
      岡山大学理学部(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Primary decompositions in abelian categories2011

    • Author(s)
      Yuji Yoshino
    • Organizer
      The 7th Japan-Vietnam Joint Seminar on Commutative Algebra
    • Place of Presentation
      Quy Nhon University, Vietnam(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Stable analogue of degenerations of Cohen-Macaulay modules2010

    • Author(s)
      Y.Yoshino
    • Organizer
      第32回可換環論シンポジウム(兼:第6回Japan-Vietnam Joint Seminar on Commutative Algebra)
    • Place of Presentation
      IPC生産性国際交流センター(神奈川県)
    • Year and Date
      2010-12-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] Degeneration of Cohen-Macaulay modules in stable category2010

    • Author(s)
      Y.Yoshino
    • Organizer
      International Conference of Representations of Algebra and Workshop XIV
    • Place of Presentation
      東京オリンピックセンター
    • Year and Date
      2010-08-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stable analogue of degenerations of Cohen-Macaulay modules2010

    • Author(s)
      吉野雄 二
    • Organizer
      第32回可換環論シンポジウム
    • Place of Presentation
      神奈川県葉山町湘南国際村
    • Related Report
      2013 Final Research Report
  • [Presentation] Degeneration of Cohen-Macaulay modules in stable category2010

    • Author(s)
      Yuji Yoshino
    • Organizer
      ICRA (International Conference of Representations of Algebra and Workshop)
    • Place of Presentation
      Tokyo
    • Related Report
      2013 Final Research Report
  • [Presentation] Local cohomology and t-structure2010

    • Author(s)
      Yuji Yoshino
    • Organizer
      The 5th Japan-Vietnam joint seminar on commutative algebra
    • Place of Presentation
      Vietnam Academy of Science and Technology, Institute of Mathematics, Hanoi, Vietnam
    • Related Report
      2013 Final Research Report
  • [Presentation] Local cohomology and t-structure2010

    • Author(s)
      Yuji Yoshino
    • Organizer
      The 5th Japan-Vietnam joint seminar on commutative algebra
    • Place of Presentation
      Vietnam Academy of Science and Tech. Hanoi
    • Related Report
      2009 Annual Research Report
  • [Presentation] Subfunctors of identity functor and t-structures2009

    • Author(s)
      吉 野 雄 二 , 吉 澤 毅
    • Organizer
      第31回可換環論シンポジウ ム
    • Place of Presentation
      ホテルアウ ィ ーナ大阪
    • Related Report
      2013 Final Research Report
  • [Presentation] Non-graded MCM modules over a graded Gorenstein ring2009

    • Author(s)
      Yuji Yoshino
    • Organizer
      京都大学数理解析研究所・ 共同利用研究集会
    • Place of Presentation
      代数的三角 圏と その周辺
    • Related Report
      2013 Final Research Report
  • [Presentation] フロベニウスの右作用と左作用2009

    • Author(s)
      吉野雄二, 吉澤毅
    • Organizer
      学会一般講演
    • Place of Presentation
      東京大学駒場キャンパス
    • Related Report
      2013 Final Research Report
  • [Presentation] 加法的部分圏の自己同型群2009

    • Author(s)
      吉野雄二, 平松直哉
    • Organizer
      学会一般講演
    • Place of Presentation
      東京大学駒場キャンパス
    • Related Report
      2013 Final Research Report
  • [Presentation] 射影次元が有限な加群への埋め込み2009

    • Author(s)
      高橋亮, Siamak Yassemi, 吉野雄二
    • Organizer
      学会一般講演
    • Place of Presentation
      東京大学駒場キャンパス
    • Related Report
      2013 Final Research Report
  • [Presentation] Auto-equivalences of additive full subcategories2009

    • Author(s)
      Yuji Yoshino
    • Organizer
      The 4th Japan-Vietnam Joint Seminar
    • Place of Presentation
      明治大学(生田)
    • Related Report
      2013 Final Research Report
  • [Presentation] Non-graded MCM modules over a graded Gorenstein ring2009

    • Author(s)
      Yuji Yoshino
    • Organizer
      京都大学数理解析研究所・共同利用研究集会「代数的三角圏とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2009 Annual Research Report
  • [Presentation] Auto-equivalences of additive full subcategories2009

    • Author(s)
      Yuji Yoshino
    • Organizer
      The 4th Japan-Vietnam joint seminar on commutative algebra
    • Place of Presentation
      明治大学
    • Related Report
      2009 Annual Research Report
  • [Presentation] Subfunctors of identity functor and t-structures2009

    • Author(s)
      Yuji Yoshino
    • Organizer
      第31回可換環論シンポジウム
    • Place of Presentation
      ホテルアウィーナ大阪
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.okayama-u.ac.Jp/~yoshino/JapaneseIndex.html

    • Related Report
      2013 Final Research Report
  • [Remarks] http://www.math.okayama-u.ac.jp/~yoshino/

    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.okayama-u.ac.jp/~yoshino/JapaneseIndex.html

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.okayama_u.ac.jp/~yoshino/JapaneseIndex.htm

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2019-07-29  

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