On stratifications and foliations on the moduli space of abelian varieties

• Project/Area Number: 21740006
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Yokohama National University (2010-2012); Kobe University (2009)
• Principal Investigator: HARASHITA Shushi 横浜国立大学, 環境情報研究院, 准教授 (70396852)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 代数幾何学 / 数論幾何学 / アーベル多様体 / モジュライ空間 / p-可除群 / 葉層構造 / 階層構造 / eligne-Lusztig多様体 / Deligne-Lusztig多様体 / 有限群スキーム / p-加除群

Research Abstract

It is important to study the moduli space of abelian varieties, as it has a wide range of applications. This research concerns the descriptions of stratifications and foliations and with relations between them. In particular we succeeded in determining the Newton polygon of the generic point of each EO-stratum and in determining the structure of EO-strata contained in the supersingular locus. Also we studied several varieties related to these strata.

Research Products

• [Journal Article] The supremum of Newton polygons of p-divisible groups with a given p-kernel type. Geometry and Analysis of Automorphic Forms of Several Variables, Proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60th birthday (2011)
  • Author(s): Shushi Harashita
  • Journal Title: Series on Number Theory and Its Applications Volume: Vol.7 Pages: 41-55
  • Peer Reviewed
• [Journal Article] The supremum of Newton polygons of p-divisible groups with a given p-kernel type (2011)
  • Author(s): Shushi Harashita
  • Journal Title: Proceedings of the international symposium in honor of Takayuki Oda on the occasion of his 60th birthday, Series on Number Theory and Its Applications Volume: 7 Pages: 41-55
  • Peer Reviewed
• [Journal Article] Generic Newton polygons of Ekedahl-Oort strata: Oort's conjecture (2010)
  • Author(s): Shushi Harashita
  • Journal Title: Annales de l'Institut Fourier Volume: 60, no5 Pages: 1787-1830
  • Peer Reviewed
• [Journal Article] Ekedahl-Oort strata contained in the supersingular locus and Deligne-Lusztig varieties. (2010)
  • Author(s): Shushi Harashita
  • Journal Title: Journal of Algebraic Geometry Volume: 19 Pages: 419-438
  • Peer Reviewed
• [Journal Article] The rings of Witt vectors for noncommutative rings with some rich structure (2010)
  • Author(s): Shushi Harashita
  • Journal Title: Communications in Algebra Volume: Vol.38 Pages: 1282-1290
• [Journal Article] Ekedahl-Oort strata contained in the supersingular locus and Deligne-Lusztig varieties (2010)
  • Author(s): Shushi Harashita
  • Journal Title: Journal of Algebraic Geometry Volume: 19 Pages: 419-438
  • Peer Reviewed
• [Journal Article] Generic Newton polygons of Ekedahl-Oort strata : Oort's conjecture (2010)
  • Author(s): Shushi Harashita
  • Journal Title: Annales de l'Institut Fourier Volume: 60 Pages: 1787-1830
  • Peer Reviewed
• [Journal Article] Configuration of the central streams in the moduli of abelian varieties (2009)
  • Author(s): Shushi Harashita
  • Journal Title: The Asian Journal of Mathematics Volume: 13 no.2 Pages: 215-250
  • Peer Reviewed
• [Journal Article] Successive extensions of minimal p-divisible groups (2009)
  • Author(s): Shushi Harashita
  • Journal Title: Journal of Pure and Applied Algebra Volume: 213 Pages: 1823-1834
  • Peer Reviewed
• [Journal Article] Configuration of the central streams in the moduli of abelian varieties (2009)
  • Author(s): Shushi Harashita
  • Journal Title: Asian Journal of Mathematics 13 Pages: 215-250
  • Peer Reviewed
• [Journal Article] Successive extensions of minimal p-divisible groups (2009)
  • Author(s): Shushi Harashita
  • Journal Title: Journal of Pure and Applied Algebra 213 Pages: 1823-1834
  • Peer Reviewed
• [Journal Article] Ekedahl-Oort strata contained in the supersingular locus and Deligne-Lusztig varieties
  • Author(s): Shushi Harashita
  • Journal Title: Journal of Algebraic Geometryに採録が決定 (掲載確定)
  • Peer Reviewed
• [Journal Article] Generic Newton polygons of Ekedahl-Oort Strata : Oort's conjecture
  • Author(s): Shushi Harashita
  • Journal Title: Annales de l'Institut Fourierに採録が決定 (掲載確定)
  • Peer Reviewed
• [Journal Article] The supremum of Newton polygons of p-divisible groups with a given p-kernel type
  • Author(s): Shushi Harashita
  • Journal Title: (投稿中)(掲載確定)
• [Presentation] 正標数の体上のアーベル多様体のモジュライ空間の葉層構造について (2013)
  • Author(s): 原下秀士
  • Organizer: 北海道大学数論幾何学セミナー
  • Place of Presentation: 北海道大学理学部3号館3-413
• [Presentation] On the affineness of fine Deligne-Lusztig varieties (2011)
  • Author(s): 原下秀士
  • Organizer: 保型形式の整数論月例セミナー(織田孝幸)
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2011-12-17
• [Presentation] On the affineness of distinguished Deligne-Lusztig varieties (2011)
  • Author(s): 原下秀士
  • Organizer: 保型形式の整数論月例セミナー
  • Place of Presentation: 東京大学大学院数理科学研究科(招待講演)
  • Year and Date: 2011-12-17
• [Presentation] On the affineness of fine Deligne-Lusztig varieties (2011)
  • Author(s): 原下秀士
  • Organizer: 代数幾何研究集会
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2011-12-07
• [Presentation] On the affineness of fine Deligne-Lusztig varieties (2011)
  • Author(s): 原下秀士
  • Organizer: 代数幾何研究集会
  • Place of Presentation: 東京大学大学院数理科学研究科(招待講演)
  • Year and Date: 2011-12-07
• [Presentation] On the affineness of fine Deligne-Lusztig varieties. 2011Taiwan-Japan Workshop on Arithmetic Algebraic Geometry and Related Topics (T. Katsura, T. Saito, C.-F. Yu) (2011)
  • Author(s): Shushi Harashita
  • Organizer: Institute of Mathematics, Academia Sinica (NTU Campus), 6F Auditorium.
  • Place of Presentation: 台湾
  • Year and Date: 2011-11-17
• [Presentation] On the affineness of fine Deligne-Lusztig varieties (2011)
  • Author(s): Shushi Harashita
  • Organizer: 2011 Taiwan-Japan Workshop on Arithmetic Algebraic Geometry and Related Topics
  • Place of Presentation: Institute of Mathematics, Academia Sinica, Taiwan(招待講演)
  • Year and Date: 2011-11-17
• [Presentation] Deligne-Lusztig varieties associated to G2. Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces (T. Ito) (2011)
  • Author(s): Shushi Harashita
  • Organizer: Department of Mathematics
  • Place of Presentation: Kyoto University Lecture Room 110
  • Year and Date: 2011-07-08
• [Presentation] Deligne-Lusztig varieties associated to G_2 (2011)
  • Author(s): Shushi Harashita
  • Organizer: Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces
  • Place of Presentation: Department of Mathematics, Kyoto University(招待講演)
  • Year and Date: 2011-07-08
• [Presentation] Optimal estimation of the Newton polygon of a p-divisible group from its p-kernel I, II (2010)
  • Author(s): 原下秀士
  • Organizer: 数論幾何学ワークショップ 2010
  • Place of Presentation: 沖縄尚学高等学校
• [Presentation] Deligne-Lusztig 多様体入門I, II (2010)
  • Author(s): 原下秀士
  • Organizer: 代数幾何研究集会2010
  • Place of Presentation: 法政大学
• [Presentation] Optimal estimation of the Newton polygon of a p-divisible group from its p-kernel I, II. (2010)
  • Author(s): 原下秀士
  • Organizer: 数論幾何学ワークショップ2010
  • Place of Presentation: 沖縄尚学高等学校
• [Presentation] Deligne-Lusztig多様体入門I,II (2010)
  • Author(s): 原下秀士
  • Organizer: 代数幾何研究集会2010
  • Place of Presentation: 法政大学
• [Presentation] Estimating the Newton polygon of a p-divisible group from its p-kernel (2009)
  • Author(s): 原下秀士
  • Organizer: 野田モジュラー多様体研究集会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2009-12-24
• [Presentation] Estimating the Newton polygon of a p-divisible group from its p-kernel (2009)
  • Author(s): 原下秀士
  • Organizer: 野田モジュラー多様体研究集会
  • Place of Presentation: 東京理科大学(千葉県)
  • Year and Date: 2009-12-24
• [Presentation] On the Siegel modular varieties of small genera in positive characteristic (2009)
  • Author(s): 原下秀士
  • Organizer: 「正標数の代数幾何学」研究集会
  • Place of Presentation: 法政大学(東京都)
  • Year and Date: 2009-12-18
• [Presentation] The optimal estimation of the Newton polygon of a p-divisible group from its p-kernel (2009)
  • Author(s): Shushi Harashita
  • Organizer: Industrious Number Theory
  • Place of Presentation: 九州大学
  • Year and Date: 2009-12-05
• [Presentation] The optimal estimation of the Newton polygon of a p-divisible group from its p-kernel (2009)
  • Author(s): Shushi Harashita
  • Organizer: Industrious Number Theory
  • Place of Presentation: 九州大学(福岡県)
  • Year and Date: 2009-12-05
• [Presentation] Estimating the Newton polygon of a p-divisible group from its p-kernel. (2009)
  • Author(s): Shushi Harashita
  • Organizer: Workshop on Arithmetic Geometry in Kanazawa(金沖数論幾何集会)
  • Place of Presentation: 石川県文教会館
  • Year and Date: 2009-11-24
• [Presentation] Estimating the Newton polygon of a p-divisible group from its p-kernel (2009)
  • Author(s): Shushi Harashita
  • Organizer: Workshop on Arithmetic Geometry in Kanazawa
  • Place of Presentation: 石川県文教会館(石川県)
  • Year and Date: 2009-11-24
• [Presentation] p-可除群のp-核と同種の関係について (2009)
  • Author(s): 原下秀士
  • Organizer: 大阪大学整数論&保型形式セミナー
  • Year and Date: 2009-11-06
• [Presentation] p-可除群のp-核と同種類の関係について (2009)
  • Author(s): 原下秀士
  • Organizer: 大阪大学整数論&保型形式セミナー
  • Place of Presentation: 大阪大学(大阪府)
  • Year and Date: 2009-11-06
• [Presentation] The supremum of Newton polygons of p-divisible groups with a given p-kernel type (2009)
  • Author(s): Shushi Harashita
  • Organizer: 代数幾何学城崎シンポジウム
  • Place of Presentation: 兵庫県立城崎大会議館
  • Year and Date: 2009-10-29
• [Presentation] The supremum of Newton polygons of p-divisible groups with a given p-kernel type (2009)
  • Author(s): Shushi Harashita
  • Organizer: 代数幾何学城崎シンポジウム
  • Place of Presentation: 兵庫県立城崎大会議館(兵庫県)
  • Year and Date: 2009-10-29
• [Presentation] p-可除群の同種類をその p- 核から最も良く評価するアルゴリズムに ついて (2009)
  • Author(s): 原下秀士
  • Organizer: 神戸大学理学部数学教室談話会
  • Year and Date: 2009-10-14
• [Presentation] p-可除群の同種類をそのp-核から最も良く評価するアルゴリズムについて (2009)
  • Author(s): 原下秀士
  • Organizer: 神戸大学理学部数学教室談話会
  • Place of Presentation: 神戸大学(兵庫県)
  • Year and Date: 2009-10-14
• [Presentation] The supremum of Newton polygons of p-divisible groups with a given p-kernel type. The international symposium, Geometry and Analysis of Automorphic Forms of Several Variables (2009)
  • Author(s): Shushi Harashita
  • Organizer: in honor of Professor Takayuki Oda on the occasion of his 60th birthday
  • Place of Presentation: 東京大学数理科学研究科大講義室
  • Year and Date: 2009-09-15
• [Presentation] The supremum of Newton polygons of p-divisible groups with a given p-kernel type (2009)
  • Author(s): Shushi Harashita
  • Organizer: The international symposium, Geometry and Analysis of Automorphic forms of Several Variables
  • Place of Presentation: 東京大学数理科学研究科(東京都)
  • Year and Date: 2009-09-15