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Comprehensive studies on Shimura varieties, arithmeticgeometry, Galois representations, and automorphic representations

Research Project

Project/Area Number 20674001
Research Category

Grant-in-Aid for Young Scientists (S)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionKyoto University

Principal Investigator

ITO Tetsushi  京都大学, 大学院・理学研究科, 准教授 (10456840)

Project Period (FY) 2008 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥38,220,000 (Direct Cost: ¥29,400,000、Indirect Cost: ¥8,820,000)
Fiscal Year 2012: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000)
Fiscal Year 2011: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000)
Fiscal Year 2010: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000)
Fiscal Year 2009: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000)
Fiscal Year 2008: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Keywords数論幾何学 / ガロア表現 / 保型表現 / 志村多様体
Research Abstract

We invited many young foreign researchers working actively on the topics related toShimura varieties, Galois representations and automorphic representations, andorganized several international workshops. We organized several workshops on recentadvanced topics for young researchers including graduate students. We actively haddiscussions and seminars with the participants, and promoted comprehensive studiesby not being obsessed with existing categories of topics. We provided new insights intothe geometry and the cohomology of Shimura varieties and Rapoport-Zink spaceswhich are local analogues of Shimura varieties.

Assessment Rating
Verification Result (Rating)

B

Report

(8 results)
  • 2013 Research Progress Assessment (Verification Result) ( PDF )
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (67 results)

All 2013 2012 2011 2010 2009 2008

All Journal Article (23 results) Presentation (44 results)

  • [Journal Article] ガロア理論と淡中‐クライン双対性2013

    • Author(s)
      伊藤哲史
    • Journal Title

      数学セミナー

      Volume: 2013 年1 月号 Pages: 18-23

    • Related Report
      2012 Final Research Report
  • [Journal Article] ガロア理論と淡中-クライン双対性2013

    • Author(s)
      伊藤哲史
    • Journal Title

      数学セミナー

      Volume: 1 Pages: 18-23

    • Related Report
      2012 Annual Research Report
  • [Journal Article] 導来圏と数論幾何 L関数, Galois表現,モチーフ2012

    • Author(s)
      伊藤哲史
    • Journal Title

      数理科学

      Volume: 8 Pages: 28-33

    • Related Report
      2012 Annual Research Report
  • [Journal Article] 解けるけど解けない方程式2012

    • Author(s)
      伊藤哲史
    • Journal Title

      大学への数学

      Volume: 12 Pages: 60-63

    • Related Report
      2012 Annual Research Report
  • [Journal Article] 非可換類体論の現状,ゼータ関数の解析接続法2011

    • Author(s)
      伊藤哲史
    • Journal Title

      数理科学

      Volume: 2011 年1 月号 Pages: 40-45

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Journal Article] 1995年:フェルマー予想解決(特集:この20年で数学に何が起こったか)2011

    • Author(s)
      伊藤哲史
    • Journal Title

      数学セミナー

      Volume: 4 Pages: 14-20

    • NAID

      40018752276

    • Related Report
      2011 Annual Research Report
  • [Journal Article] 数論幾何におけるガロア理論(特集:ガロア生誕200年)2011

    • Author(s)
      伊藤哲史
    • Journal Title

      数学セミナー

      Volume: 10 Pages: 21-25

    • NAID

      40018979800

    • Related Report
      2011 Annual Research Report
  • [Journal Article] 素数を数える2011

    • Author(s)
      伊藤哲史
    • Journal Title

      大学への数学

      Volume: 8 Pages: 68-71

    • Related Report
      2011 Annual Research Report
  • [Journal Article] 非可換類体論の現状,ゼータ関数の解析接続法2011

    • Author(s)
      伊藤哲史
    • Journal Title

      数理科学 2011年1月号

      Pages: 40-45

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 直角三角形の不思議な世界2011

    • Author(s)
      伊藤哲史
    • Journal Title

      大学への数学 2011年1月号

      Pages: 64-67

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 直角三角形の不思議な世界2011

    • Author(s)
      伊藤哲史
    • Journal Title

      大学への数学

      Volume: 54 Pages: 64-67

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 合同ゼータのリーマン予想とその発展・影響2009

    • Author(s)
      伊藤哲史
    • Journal Title

      数学セミナー

      Volume: 2009 年11月号 Pages: 18-23

    • Related Report
      2012 Final Research Report
  • [Journal Article] 有限体上の楕円曲線の有理点ハッセの定理2009

    • Author(s)
      伊藤哲史
    • Journal Title

      数学書房編「この定理が美しい」

      Pages: 20-29

    • Related Report
      2012 Final Research Report
  • [Journal Article] 合同ゼータのリーマン予想とその発展・影響2009

    • Author(s)
      伊藤哲史
    • Journal Title

      数学セミナー(日本評論社) 2009年11月号

      Pages: 18-23

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 有限体上の楕円曲線の有理点ハッセの定理2009

    • Author(s)
      伊藤哲史
    • Journal Title

      この定理が美しい(数学書房)

      Pages: 20-29

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 有限体上の楕円曲線の有理点 ハッセの定理2009

    • Author(s)
      伊藤哲史
    • Journal Title

      この定理が美しい

      Pages: 20-29

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 佐藤-テイト予想, ついに完全解決か?!2009

    • Author(s)
      伊藤哲史
    • Journal Title

      数学セミナー 9月号

      Pages: 34-35

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 合同ゼータのリーマン予想とその発展・影響2009

    • Author(s)
      伊藤哲史
    • Journal Title

      数学セミナー 11月号

      Pages: 18-23

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 佐藤‐テイト予想の証明の方針2008

    • Author(s)
      伊藤哲史
    • Journal Title

      数学のたのしみ2008 最終号, 日本評論社

      Volume: 2008 最終号 Pages: 118-132

    • Related Report
      2012 Final Research Report
  • [Journal Article] 佐藤-テイト予想の証明の方針2008

    • Author(s)
      伊藤哲史
    • Journal Title

      数学のたのしみ(日本評論社) 2008最終号

      Pages: 118-132

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 楕円曲線入門2008

    • Author(s)
      伊藤哲史
    • Journal Title

      数学のたのしみ2008最終号

      Pages: 35-53

    • Related Report
      2008 Annual Research Report
  • [Journal Article] 佐藤-テイト予想の証明の方針2008

    • Author(s)
      伊藤哲史
    • Journal Title

      数学のたのしみ2008最終号

      Pages: 118-132

    • Related Report
      2008 Annual Research Report
  • [Journal Article] ガロア表現の変形理論をヘッケ論をヘッケ環2008

    • Author(s)
      伊藤哲史
    • Journal Title

      数学のたのしみ2008最終号

      Pages: 133-145

    • Related Report
      2008 Annual Research Report
  • [Presentation] Supercuspidalrepresentations in the cohomology of theRapoport-Zink space for the unitary groupin three variables2013

    • Author(s)
      伊藤哲史
    • Organizer
      AutomorphicRepresentations and Related Topics
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-01-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Supercuspidal representations in the cohomology of the Rapoport-Zink space for the unitary group in three variables2013

    • Author(s)
      伊藤哲史
    • Organizer
      Automorphic Representations and Related Topics
    • Place of Presentation
      京都大学数理解析研究所(招待講演)
    • Year and Date
      2013-01-23
    • Related Report
      2012 Annual Research Report
  • [Presentation] Supercuspidalrepresentations in the cohomology of theRapoport-Zink space for the unitary groupin three variables2013

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on Modularforms and Galois Representations
    • Place of Presentation
      Korea Institute for AdvancedStudy, 韓国
    • Year and Date
      2013-01-07
    • Related Report
      2012 Final Research Report
  • [Presentation] Supercuspidal representations in the cohomology of the Rapoport-Zink space for the unitary group in three variables2013

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on Modular forms and Galois representations
    • Place of Presentation
      Korea Institute for Advanced Study (韓国)(招待講演)
    • Year and Date
      2013-01-07
    • Related Report
      2012 Annual Research Report
  • [Presentation] Rapoport-Zink spaces and endoscopy2012

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on the arithmetic geometry of Shimura varieties representation theory, and related topics
    • Place of Presentation
      北海道大学大学院理学研究院数学部門
    • Year and Date
      2012-07-18
    • Related Report
      2012 Annual Research Report
  • [Presentation] 非可換局所類体論の幾何的実現について2012

    • Author(s)
      伊藤哲史
    • Organizer
      大岡山談話会
    • Place of Presentation
      東京工業大学大学院理工学研究科数学専攻
    • Year and Date
      2012-07-04
    • Related Report
      2012 Annual Research Report
  • [Presentation] Endoscopy and the l-adic cohomology of the Rapoport-Zink space for GSp (4)2012

    • Author(s)
      伊藤哲史
    • Organizer
      University of Chicago Number Theory Seminar
    • Place of Presentation
      University of Chicago (アメリカ)
    • Year and Date
      2012-05-16
    • Related Report
      2012 Annual Research Report
  • [Presentation] Endoscopy and the l-adic cohomology of the Rapoport-Zink space for GSp (4)2012

    • Author(s)
      伊藤哲史
    • Organizer
      Northwestern Number Theory Seminar
    • Place of Presentation
      Northwestern University(アメリカ)
    • Year and Date
      2012-05-14
    • Related Report
      2012 Annual Research Report
  • [Presentation] p進体上のユニタリ群のRapoport-Zink空間と超尖点的表現について2012

    • Author(s)
      伊藤哲史
    • Organizer
      定山渓数論的表現論研究集会
    • Place of Presentation
      定山渓温泉研修保養施設倶楽部錦渓
    • Year and Date
      2012-01-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] p-adic uniformization ofShimura varieties and applications2012

    • Author(s)
      伊藤哲史
    • Organizer
      KIAS Intensive Lecture Series on RigidGeometry and the Local Langlandscorrespondence
    • Place of Presentation
      KoreaInstitute for Advanced Study, 韓国.
    • Year and Date
      2012-01-05
    • Related Report
      2012 Final Research Report
  • [Presentation] p-adic uniformization of Shimura varieties and applications2012

    • Author(s)
      伊藤哲史
    • Organizer
      KIAS Intensive Lecture Series on Rigid Geometry and the Local Langlands correspondence
    • Place of Presentation
      Korea Institute for Advanced Study
    • Year and Date
      2012-01-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] 局所Langlands対応の幾何的実現について2011

    • Author(s)
      伊藤哲史
    • Organizer
      北海道大学大学院理学研究院数学部門大談話会
    • Place of Presentation
      北海道大学大学院理学研究院数学部門
    • Year and Date
      2011-11-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] l-adic cohomology ofRapoport-Zink spaces and supercuspidalpackets2011

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on the arithmeticgeometry of Shimura varieties andRapoport-Zink spaces
    • Place of Presentation
      京都大学数学教室.
    • Year and Date
      2011-07-07
    • Related Report
      2012 Final Research Report
  • [Presentation] 1-adic cohomology of Rapoport-Zink spaces and supercuspidal packets2011

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces
    • Place of Presentation
      京都大学大学院理学研究科数学教室
    • Year and Date
      2011-07-07
    • Related Report
      2011 Annual Research Report
  • [Presentation] Shimura varieties and Rapoport-Zink spaces---an introduction2011

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces
    • Place of Presentation
      京都大学大学院理学研究科数学教室
    • Year and Date
      2011-07-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Voganによる局所Langlands予想の精密化2010

    • Author(s)
      伊藤哲史
    • Organizer
      別府数論幾何集会
    • Place of Presentation
      別府国際コンベンションセンター
    • Year and Date
      2010-11-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the l-adic cohomology ofthe Rapoport-Zink space for GSp(4)2010

    • Author(s)
      伊藤哲史
    • Organizer
      TheSecond PANT (PanAsian Number Theory)Conference
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-09-16
    • Related Report
      2012 Final Research Report
  • [Presentation] On the l-adic cohomology of the Rapoport-Zink space for GSp (4)2010

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「The Second PANT (PanAsian Number Theory) Conference」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-09-16
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On the 1-adic cohomology of the Rapoport-Zink space for GSp(4)2010

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「The Second PANT(PanAsian Number Theory)Conference」
    • Place of Presentation
      京都大学数理解析研究所(招待講演)
    • Year and Date
      2010-09-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the order of vanishing ofautomorphic L-functions for GL(2) over global fields at the center of functionalequation2010

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on arithmeticgeometry and related topics
    • Place of Presentation
      National Taiwan University, 台湾.
    • Year and Date
      2010-07-12
    • Related Report
      2012 Final Research Report
  • [Presentation] On the order of vanishing of automorphic L-functions for GL (2) over global fields at the center of functional equation2010

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「Workshop on arithmetic geometry and related topics」
    • Place of Presentation
      National Taiwan University, 台湾
    • Year and Date
      2010-07-12
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On the order of vanishing of automorphic L-functions for GL(2)over global fields at the center of functional equation2010

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「Workshop on arithmetic geometry and related topics」
    • Place of Presentation
      National Taiwan University(台湾)(招待講演)
    • Year and Date
      2010-07-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] 平方数の和で表される素数について2010

    • Author(s)
      伊藤哲史
    • Organizer
      城崎新人セミナー
    • Place of Presentation
      城崎健康福祉センター
    • Year and Date
      2010-02-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] Introduction to modular forms and non-abelian class field theory2010

    • Author(s)
      伊藤哲史
    • Organizer
      First friendship meeting in mathematics between Fudan and Kyoto Universities
    • Place of Presentation
      京都大学時計台記念ホール
    • Year and Date
      2010-01-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] Shimura varieties on the unitary group GU(n, n)Galois representations associated to automorphic forms on GU(n, n)I, II2010

    • Author(s)
      伊藤哲史
    • Organizer
      Study workshop on the work of Skinner-Urban on the Iwasawa main conjecture for GL(2)
    • Place of Presentation
      The Chinese University of Hong Kong(香港中文大学)(香港)
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the history of the Sato-Tate conjecture2009

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「金沢数論幾何集会」
    • Place of Presentation
      石川県文教会館
    • Year and Date
      2009-11-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] Rational curves and the moduli space of abelian surfaces in characteristic p2009

    • Author(s)
      伊藤哲史
    • Organizer
      研究集会「代数幾何の関連する諸分野」
    • Place of Presentation
      北海道大学理学部
    • Year and Date
      2009-09-02
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the weak Lefschetz theorem for singular varieties and the supersingular strata of Siegel threefolds2009

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「p-adic Automorphic Forms and Arithmetic Geometry」
    • Place of Presentation
      大島開発総合センター
    • Year and Date
      2009-07-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] Logarithmic geometry andDeligne-Rapoport's integral models2009

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on Automorphic Representations,Geometry, and Arithmetic
    • Place of Presentation
      National Taiwan University, 台湾.
    • Year and Date
      2009-07-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Logarithmic geometry and Deligne-Rapoport's integral models2009

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「Workshop on Automorphic Representations, Geometry, and Arithmetic」
    • Place of Presentation
      National Taiwan University, 台湾
    • Year and Date
      2009-07-23
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Logarithmic geometry and Deligne-Rapoport's integral models2009

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「Workshop on Automorphic Representations, Geometry, and Arithmetic」
    • Place of Presentation
      National Taiwan University (台湾)
    • Year and Date
      2009-07-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the cohomology ofsupersingular loci of Siegel threefolds2009

    • Author(s)
      伊藤哲史
    • Organizer
      p-adic Hodge theory, p-adic modular formsand applications
    • Place of Presentation
      Centrede Conferences de la Station de Biologie,Marine, Roscoff, フランス
    • Year and Date
      2009-07-14
    • Related Report
      2012 Final Research Report
  • [Presentation] On the cohomology ofsupersingular loci of Siegel threefolds2009

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「p-adic Hodge theory, p-adicmodular forms and applications」
    • Place of Presentation
      Centre de Conferences de la Station de Biologie, Marine, Roscoff, フランス
    • Year and Date
      2009-07-14
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On the cohomology of supersingular loci of Siegel threefolds2009

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「p-adic Hodge theory, p-adic modular forms and applications」
    • Place of Presentation
      Centre de Conferences de la Station de Biologie Marine, Roscoff (フランス)
    • Year and Date
      2009-07-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] 佐藤-デイト予想の解決と展望2009

    • Author(s)
      伊藤哲史
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the Sato-Tate conjecture for elliptic curves over number fields which are not necessarily totally real2009

    • Author(s)
      伊藤哲史
    • Organizer
      愛媛整数論集会
    • Place of Presentation
      愛媛大学理学部数学教室
    • Year and Date
      2009-02-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the l-adic cohomology ofSiegel threefolds in characteristic p2009

    • Author(s)
      伊藤哲史
    • Organizer
      PANT 2009 - Pohang, Pan Asian Number TheoryConference
    • Place of Presentation
      POSTECH(浦項工科大学), 韓国
    • Year and Date
      2009-01-10
    • Related Report
      2012 Final Research Report
  • [Presentation] On the l-adic cohomology of Siegel threefolds in characteristic p2009

    • Author(s)
      伊藤哲史
    • Organizer
      国際研究集会「PANT 2009-Pohang, Pan Asian Number Theory Conference」
    • Place of Presentation
      POSTECH (浦項工科大学),韓国
    • Year and Date
      2009-01-10
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On the l-adic cohomology of Siegel threefolds in characteristic p2009

    • Author(s)
      伊藤哲史
    • Organizer
      PANT 2009-Pohang, Pan Asian Number Theory Conference
    • Place of Presentation
      浦項工科大学数学科(韓国)
    • Year and Date
      2009-01-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the l-adic cohomology ofSiegel threefolds in characteristic p2008

    • Author(s)
      伊藤哲史
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      京都大学数理解析研究所.
    • Year and Date
      2008-12-09
    • Related Report
      2012 Final Research Report
  • [Presentation] On the l-adic cohomology of Siegel threefolds in characteristic p2008

    • Author(s)
      伊藤哲史
    • Organizer
      研究集会「代数的整数論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-12-09
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On the l-adic cohomology of Siegel threefolds in characteristic p2008

    • Author(s)
      伊藤哲史
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-12-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] Construction of Galois representations I-The fundamental lemma (after Laumon-Ngo)2008

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on Shimura Varieties, Automorphic Representations and Related Topics
    • Place of Presentation
      京都大学理学研究科数学教室
    • Year and Date
      2008-11-28
    • Related Report
      2008 Annual Research Report
  • [Presentation] Introduct ion to Shimura varieties2008

    • Author(s)
      伊藤哲史
    • Organizer
      Workshop on Shimura Varieties, Automorphic Representations and Related Topics
    • Place of Presentation
      京都大学理学研究科数学教室
    • Year and Date
      2008-11-25
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2019-07-29  

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