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2014 Fiscal Year Research-status Report

非可換クレパント解消、オービフォールド・コホモロジーとマッカイ対応の一般化

Research Project

Project/Area Number 23540045
Research InstitutionNagoya University

Principal Investigator

伊藤 由佳理  名古屋大学, 多元数理科学研究科, 准教授 (70285089)

Co-Investigator(Kenkyū-buntansha) 伊山 修  名古屋大学, 多元数理科学研究科, 教授 (70347532)
長尾 健太郎  名古屋大学, 多元数理科学研究科, 助教 (10585574) [Withdrawn]
Project Period (FY) 2011-04-28 – 2017-03-31
Keywords特異点解消 / マッカイ対応 / 三角圏
Outline of Annual Research Achievements

研究代表者である伊藤由佳理は, 昨年度までのクレパントな特異点解消の存在についての予想を確かめる例をたくさん計算した. その結果, トリヘドラルと呼ばれる場合に関しては, Reidのレシピと呼ばれる具体的な幾何学的マッカイ対応が非可換な群に対しても成り立ちそうなことを確かめられた. また, その周辺の問題について, 9月のイギリス・ウォーリック大学での研究集会で研究成果と予想について 講演した. その予想について, 参加者の一人であったイギリス・バース大学の Alastair Craw 氏と 3 次元マッ カイ対応の共同研究を開始した.
また研究分担者の伊山修氏は, Dong Yangとの共同研究で, 三角圏の特別な商の構成方法である準傾退化(silting reduction)を導入し, 基本的な性質を調べた. 準傾退化の主要な性質は, Verdier商であると同時に, 部分圏のイデアル商として実現することも可能な点である. さらにこれを特別な三角圏Tから団圏(cluster category)Cを構成するAmiot-Guo-Keller構成に適用し, Tの準傾退化とCのCalabi-Yau退化が互換性を有することを示した.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

国際的な共同研究集会にて研究成果を発表し, さらに共同研究もいくつか行なっており, 活発な研究活動を行なっている. また, 周囲の学生やポスドクなどとの研究交流も盛んであり, 本研究課題に関連する研究もいくつか進んでいるため.

Strategy for Future Research Activity

来年度は本研究課題の最終年度であるため, 本研究課題の研究成果をとりまとめる必要がある. またマッカイ対応関連の国際的な研究集会を開催するなどして,これまでの研究成果の発表と関連する研究の最新情報の取得,情報収集も行いたい.

Causes of Carryover

予定した研究集会の開催を参加者や会場の都合等で次年度に見送ったため。

Expenditure Plan for Carryover Budget

研究集会開催予定。

  • Research Products

    (37 results)

All 2104 2015 2014

All Journal Article (14 results) (of which Peer Reviewed: 14 results,  Acknowledgement Compliant: 14 results) Presentation (20 results) (of which Invited: 16 results) Book (3 results)

  • [Journal Article] tau-tilting theory2104

    • Author(s)
      Takahide Adachi, Osamu Iyama, Idun Reiten
    • Journal Title

      Compos. Math.

      Volume: 150 Pages: 415-452

    • DOI

      10.1112/S0010437X13007422

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Existence of crepant resolutions2015

    • Author(s)
      Toshihiro Hayashi, Yukari Ito and Yuhi Sekiya
    • Journal Title

      Advanced Study in Mathematics

      Volume: - Pages: -

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Non-commutative resolutions and Grothendieck groups2015

    • Author(s)
      Hailong Dao, Osamu Iyama, Ryo Takahashi, Charles Vial
    • Journal Title

      J. Noncommut. Geom.

      Volume: 9 Pages: 21-34

    • DOI

      10.4171/JNCG/186

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Stable categories of Cohen-Macaulay modules and cluster categories2015

    • Author(s)
      Claire Amiot, Osamu Iyama, Idun Reiten
    • Journal Title

      Amer. J. Math.

      Volume: 137 Pages: -

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Reduction of triangulated categories and maximal modification algebras for cA_n singularities2015

    • Author(s)
      Osamu Iyama, Michael Wemyss
    • Journal Title

      J. Reine Angew. Math.

      Volume: - Pages: -

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Tilting bundles on orders on P^d2015

    • Author(s)
      Osamu Iyama, Boris Lerner
    • Journal Title

      Israel J. Math.

      Volume: - Pages: -

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Lattice structure of torsion classes for path algebras2015

    • Author(s)
      Osamu Iyama, Idun Reiten, Gordana Todorov, Hugh Thomas
    • Journal Title

      Bull. Lond. Math. Soc.

      Volume: - Pages: -

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Dimension of triangulated categories with respect to subcategories2014

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

      J. Algebra

      Volume: 399 Pages: 205-219

    • DOI

      10.1016/j.jalgebra.2013.09.035

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] n-representation infinite algebras2014

    • Author(s)
      Martin Herschend, Osamu Iyama, Steffen Oppermann
    • Journal Title

      Adv. Math.

      Volume: 252 Pages: 292-342

    • DOI

      10.1016/j.aim.2013.09.023

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Singular Derived Categories of Q-factorial terminalizations and Maximal Modification Algebras2014

    • Author(s)
      Osamu Iyama, Michael Wemyss
    • Journal Title

      Adv. Math.

      Volume: 261 Pages: 85-121

    • DOI

      10.1016/j.aim.2014.04.001

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Introduction to tau-tilting theory2014

    • Author(s)
      Osamu Iyama, Idun Reiten
    • Journal Title

      Proc. Natl. Acad. Sci. USA

      Volume: 111 Pages: 9704-9711

    • DOI

      10.1073/pnas.1313075111

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Maximal modifications and Auslander-Reiten duality for non-isolated singularities2014

    • Author(s)
      Osamu Iyama, Michael Wemyss
    • Journal Title

      Invent. Math.

      Volume: 197 Pages: 521-586

    • DOI

      10.1007/s00222-013-0491-y

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Intermediate co-t-structures, two-term silting objects, tau-tilting modules, and torsion classes2014

    • Author(s)
      Osamu Iyama, Peter Jorgensen, Dong Yang
    • Journal Title

      Algebra Number Theory

      Volume: 8 Pages: 2413-2431

    • DOI

      10.2140/ant.2014.8.2413

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Frobenius categories, Gorenstein algebras and rational surface singularities2014

    • Author(s)
      Martin Kalck, Osamu Iyama, Michael Wemyss, Dong Yang
    • Journal Title

      Compos. Math.

      Volume: 151 Pages: 502-534

    • DOI

      10.1112/S00104337X14007647

    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Higher preprojective algebrars and Cohen-Macaulay representations2015

    • Author(s)
      Osamu Iyama
    • Organizer
      Algebra and Geometry seminar
    • Place of Presentation
      Uppsala University, Sweden
    • Year and Date
      2015-03-24
    • Invited
  • [Presentation] Tilting theory and Cohen-Macaulay representations2015

    • Author(s)
      Osamu Iyama
    • Organizer
      Algebra seminar
    • Place of Presentation
      Mittag-Leffler Institute, Sweden
    • Year and Date
      2015-03-19
    • Invited
  • [Presentation] Higher representation-finite algebras2015

    • Author(s)
      Osamu Iyama
    • Organizer
      Higher seminars in the subject Mathematics/Applied Mathematics
    • Place of Presentation
      Mälardalens högskola, Västerås, Sweden
    • Year and Date
      2015-03-18
    • Invited
  • [Presentation] Silting reduction and Calabi-Yau reduction of triangulated categories2015

    • Author(s)
      Osamu Iyama
    • Organizer
      Homological bonds between Commutative Algebra and Representation Theory​
    • Place of Presentation
      CRM, Barcelona, Spain
    • Year and Date
      2015-02-19
    • Invited
  • [Presentation] Tilting theory and Cohen-Macaulay representations(4回連続講演)2015

    • Author(s)
      Osamu Iyama
    • Organizer
      (Re)emerging methods in Commutative Algebra and Representation Theory​
    • Place of Presentation
      CRM, Barcelona, Spain
    • Year and Date
      2015-02-09 – 2015-02-13
    • Invited
  • [Presentation] Preprojective algebras and Cohen-Macaulay representations2015

    • Author(s)
      Osamu Iyama
    • Organizer
      第27回可換環論セミナー
    • Place of Presentation
      静岡大学
    • Year and Date
      2015-01-25
  • [Presentation] Calabi-Yau reduction of cluster categories2015

    • Author(s)
      Osamu Iyama
    • Organizer
      Workshop Rikkyo MathPhys 2015
    • Place of Presentation
      立教大学
    • Year and Date
      2015-01-11
    • Invited
  • [Presentation] Orlov’s theorem and Geigle-Lenzing complete intersections2014

    • Author(s)
      Osamu Iyama
    • Organizer
      Workshop on Homological Interactions between Representation Theory and Singularity Theory
    • Place of Presentation
      Edinburgh, Scotland, U.K
    • Year and Date
      2014-12-16
    • Invited
  • [Presentation] Silting reduction and Calabi-Yau reduction of triangulated categories2014

    • Author(s)
      Osamu Iyama
    • Organizer
      第5回岡山可換代数表現セミナー
    • Place of Presentation
      岡山大学
    • Year and Date
      2014-12-08
    • Invited
  • [Presentation] Preprojective algebras and Cohen-Macaulay representations2014

    • Author(s)
      Osamu Iyama
    • Organizer
      36th symposium on Commutative Algebra
    • Place of Presentation
      International Productivity Center, Kanagawa, Japan
    • Year and Date
      2014-11-22
  • [Presentation] Higher Auslander correspondence and d-Cohen-Macaulay finiteness2014

    • Author(s)
      Osamu Iyama
    • Organizer
      Maurice Auslander Memorial Workshop
    • Place of Presentation
      University Bielefeld, Germany
    • Year and Date
      2014-11-13
    • Invited
  • [Presentation] tau-tilting theory I, II(2回講演)2014

    • Author(s)
      Osamu Iyama
    • Organizer
      Cluster algebras and Representation theory
    • Place of Presentation
      Center for Mathematical Challenges (CMC), KIAS, Seoul, Korea
    • Year and Date
      2014-11-03 – 2014-11-05
    • Invited
  • [Presentation] Cohen-Macaulay representations of Geigle-Lenzing complete intersections2014

    • Author(s)
      Osamu Iyama
    • Organizer
      可換環論と表現論
    • Place of Presentation
      岡山大学
    • Year and Date
      2014-10-13
    • Invited
  • [Presentation] Open problems on quivers and resolutions of singularities2014

    • Author(s)
      Yukari Ito
    • Organizer
      Workshop “ McKay correspondence, orbifolds, quivers
    • Place of Presentation
      Universityof Warwick, UK
    • Year and Date
      2014-09-18 – 2014-09-18
    • Invited
  • [Presentation] Silting reduction of triangulated categories2014

    • Author(s)
      Osamu Iyama
    • Organizer
      47th symposium on Ring Theory and Representation Theory
    • Place of Presentation
      Osaka City University, Japan
    • Year and Date
      2014-09-13
  • [Presentation] Cohen-Macaulay representations of Geigle-Lenzing complete intersections2014

    • Author(s)
      Osamu Iyama
    • Organizer
      XVI International Conference on Representations of Algebras (ICRA 2014)
    • Place of Presentation
      Sanya, Hainan Province, China
    • Year and Date
      2014-08-29
    • Invited
  • [Presentation] Cohen-Macaulay representations of Geigle-Lenzing complete intersections2014

    • Author(s)
      Osamu Iyama
    • Organizer
      Commutative Algebra and Singularity Theory 2014
    • Place of Presentation
      Tateyama Kokusai Hotel, Japan
    • Year and Date
      2014-07-30
    • Invited
  • [Presentation] Cohen-Macaulay representations of Geigle-Lenzing complete intersections2014

    • Author(s)
      Osamu Iyama
    • Organizer
      Advances in Representation Theory of Algebras (ARTA)
    • Place of Presentation
      Universite du Quebec a Montreal, Quebec, Canada
    • Year and Date
      2014-06-19
    • Invited
  • [Presentation] Cohen-Macaulay representations of Geigle-Lenzing complete intersections2014

    • Author(s)
      Osamu Iyama
    • Organizer
      Colloquium in honour of the 75th birthday of Helmut Lenzing
    • Place of Presentation
      Bielefeld University, Germany
    • Year and Date
      2014-05-16
    • Invited
  • [Presentation] Cohen-Macaulay representations of Geigle-Lenzing complete intersections2014

    • Author(s)
      Osamu Iyama
    • Organizer
      特異点セミナー
    • Place of Presentation
      日本大学
    • Year and Date
      2014-04-21
  • [Book] 「日本の国際化に向けて!」, “ coffee break ”, 『数学セミナー』2014 年 5 月号2014

    • Author(s)
      伊藤 由佳理
    • Total Pages
      1
    • Publisher
      日本評論社
  • [Book] 「トーラス碁をやってみよう!」『数学セミナー』2014 年 5 月号2014

    • Author(s)
      伊藤 由佳理
    • Total Pages
      4
    • Publisher
      日本評論社
  • [Book] 「女性が活躍できる環境を!」, “ coffee break ”, 『数学セミナー』2014 年 11 月号2014

    • Author(s)
      伊藤 由佳理
    • Total Pages
      1
    • Publisher
      日本評論社

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Published: 2016-05-27  

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