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

• Project/Area Number: 20674001
• Research Category: Grant-in-Aid for Young Scientists (S)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kyoto 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: ¥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

Research Products

• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [Presentation] Supercuspidalrepresentations in the cohomology of theRapoport-Zink space for the unitary groupin three variables (2013)
  • 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
• [Presentation] Supercuspidal representations in the cohomology of the Rapoport-Zink space for the unitary group in three variables (2013)
  • 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
• [Presentation] Supercuspidalrepresentations in the cohomology of theRapoport-Zink space for the unitary groupin three variables (2013)
  • 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
• [Presentation] Supercuspidal representations in the cohomology of the Rapoport-Zink space for the unitary group in three variables (2013)
  • 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
• [Presentation] Rapoport-Zink spaces and endoscopy (2012)
  • 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
• [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
• [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
• [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
• [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
• [Presentation] p-adic uniformization ofShimura varieties and applications (2012)
  • 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
• [Presentation] p-adic uniformization of Shimura varieties and applications (2012)
  • 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
• [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
• [Presentation] l-adic cohomology ofRapoport-Zink spaces and supercuspidalpackets (2011)
  • 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
• [Presentation] 1-adic cohomology of Rapoport-Zink spaces and supercuspidal packets (2011)
  • 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
• [Presentation] Shimura varieties and Rapoport-Zink spaces---an introduction (2011)
  • 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
• [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
• [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
• [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
• [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
• [Presentation] On the order of vanishing ofautomorphic L-functions for GL(2) over global fields at the center of functionalequation (2010)
  • 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
• [Presentation] On the order of vanishing of automorphic L-functions for GL (2) over global fields at the center of functional equation (2010)
  • 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
• [Presentation] On the order of vanishing of automorphic L-functions for GL(2)over global fields at the center of functional equation (2010)
  • 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
• [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
• [Presentation] Introduction to modular forms and non-abelian class field theory (2010)
  • 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
• [Presentation] Shimura varieties on the unitary group GU(n, n)Galois representations associated to automorphic forms on GU(n, n)I, II (2010)
  • 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)
• [Presentation] On the history of the Sato-Tate conjecture (2009)
  • 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
• [Presentation] Rational curves and the moduli space of abelian surfaces in characteristic p (2009)
  • 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
• [Presentation] On the weak Lefschetz theorem for singular varieties and the supersingular strata of Siegel threefolds (2009)
  • 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
• [Presentation] Logarithmic geometry andDeligne-Rapoport's integral models (2009)
  • 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
• [Presentation] Logarithmic geometry and Deligne-Rapoport's integral models (2009)
  • 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
• [Presentation] Logarithmic geometry and Deligne-Rapoport's integral models (2009)
  • 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
• [Presentation] On the cohomology ofsupersingular loci of Siegel threefolds (2009)
  • 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
• [Presentation] On the cohomology ofsupersingular loci of Siegel threefolds (2009)
  • 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
• [Presentation] On the cohomology of supersingular loci of Siegel threefolds (2009)
  • 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
• [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
• [Presentation] On the Sato-Tate conjecture for elliptic curves over number fields which are not necessarily totally real (2009)
  • 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
• [Presentation] On the l-adic cohomology ofSiegel threefolds in characteristic p (2009)
  • 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
• [Presentation] On the l-adic cohomology of Siegel threefolds in characteristic p (2009)
  • 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
• [Presentation] On the l-adic cohomology of Siegel threefolds in characteristic p (2009)
  • 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
• [Presentation] On the l-adic cohomology ofSiegel threefolds in characteristic p (2008)
  • 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
• [Presentation] On the l-adic cohomology of Siegel threefolds in characteristic p (2008)
  • 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
• [Presentation] On the l-adic cohomology of Siegel threefolds in characteristic p (2008)
  • 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
• [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
• [Presentation] Introduct ion to Shimura varieties (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: 2008-11-25