Arithmetic of hyperbolic algebraic curves related to arithmetic fundamental groups

• Project/Area Number: 15K04780
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Hoshi Yuichiro 京都大学, 数理解析研究所, 准教授 (50456761)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 双曲的代数曲線 / 数論的基本群 / 遠アーベル幾何学 / p進Teichmuller理論 / 休眠乍 / 等分点 / 巾零通常固有束 / 射影構造 / 単遠アーベル的復元アルゴリズム / 超特異因子 / Frobenius的射影構造 / 圏論的特徴付け / 副p絶対遠アーベル幾何学 / 遠アーベル予想 / 組み合わせ論的遠アーベル幾何学 / GT群 / 単遠アーベル幾何学 / Grothendieck予想 / 双曲的多重曲線 / 当分点 / 有限平坦可換群スキーム / 対数スキーム / 狭義射

Outline of Final Research Achievements

(1) I proved uniqueness of dormant opers of rank p-1 on a projective hyperbolic curves in characteristic p. (2) I studied torsion points on algebraic curves that have good reduction over absolutely unramified bases. (3) I obtained a certain categorical representation of log schemes. (4) I obtained categorical characterizations of isomorphism classes of local fields. (5) I established a pro-p criterion for good reduction of ordinary curves. (6) I solved the anabelian conjecture for moduli spaces of elliptic curves equipped with additional data. (7) I developed combinatorial anabelian geometry. (8) I gave a characterization of supersingular divisors of nilpotent ordinary indigenous bundles. (9) I established a certain positive characteristic analogue of theory of projective structures on Riemann surfaces. (10) I studied the anabelian geometry of local fields.

Research Products

• [Journal Article] On ramified torsion points on a curve with stable reduction over an absolutely unramified base (2017)
  • Author(s): Hoshi Yuichiro
  • Journal Title: Osaka Journal of Mathematics Volume: 54 Pages: 767-787
  • NAID: 120006358872
  • Peer Reviewed / Open Access
• [Journal Article] The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one (2017)
  • Author(s): Hoshi Yuichiro、Kinoshita Ryo、Nakayama Chikara
  • Journal Title: Kodai Mathematical Journal Volume: 40 Issue: 3 Pages: 625-637
  • DOI: 10.2996/kmj/1509415237
  • NAID: 130006898706
  • ISSN: 0386-5991, 1881-5472
  • Peer Reviewed / Open Access
• [Journal Article] Categorical characterization of strict morphisms of fs log schemes (2017)
  • Author(s): Yuichiro Hoshi and Chikara Nakayama
  • Journal Title: Mathematical Journal of Okayama University Volume: 59 Pages: 1-19
  • NAID: 120005898804
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] ON THE GROTHENDIECK CONJECTURE FOR AFFINE HYPERBOLIC CURVES OVER KUMMER-FAITHFUL FIELDS (2017)
  • Author(s): Yuichiro Hoshi
  • Journal Title: Kyushu Journal of Mathematics Volume: 71 Issue: 1 Pages: 1-29
  • DOI: 10.2206/kyushujm.71.1
  • NAID: 130005666217
  • ISSN: 1340-6116, 1883-2032
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Finiteness of the moderate rational points of once-punctured elliptic curves (2016)
  • Author(s): Yuichiro Hoshi
  • Journal Title: Hokkaido Mathematical Journal Volume: 45 Issue: 2 Pages: 271-291
  • DOI: 10.14492/hokmj/1470139405
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On the kernels of the pro-l outer Galois representations associated to hyperbolic curves over number fields (2015)
  • Author(s): Yuichiro Hoshi
  • Journal Title: Osaka Journal of Mathematics Volume: 52 Pages: 647-677
  • NAID: 120005830451
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Nilpotent admissible indigenous bundles via Cartier operators in characteristic three (2015)
  • Author(s): Yuichiro Hoshi
  • Journal Title: Kodai Mathematical Journal Volume: 38 Issue: 3 Pages: 690-731
  • DOI: 10.2996/kmj/1446210603
  • NAID: 130005475924
  • ISSN: 0386-5991, 1881-5472
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] A pro-p group-theoretic criterion for good reduction of ordinary proper hyperbolic curves (2018)
  • Author(s): 星裕一郎
  • Organizer: The 7th East Asia Number Theory Conference
  • Int'l Joint Research / Invited
• [Presentation] ある p 進局所体の絶対 Galois 群の外部自己同型群における体論的部分群の非正規性 (2018)
  • Author(s): 星裕一郎
  • Organizer: 東工大 数論・幾何学セミナー
• [Presentation] A simple purely group-theoretic characterization of the Grothendieck-Teichmuller group (2017)
  • Author(s): 星裕一郎
  • Organizer: Nilpotent Fundamental Groups
  • Int'l Joint Research / Invited
• [Presentation] On torsion points on a curve with good reduction over an absolutely unramified base (2017)
  • Author(s): 星裕一郎
  • Organizer: Oberseminar Algebra und Geometrie
• [Presentation] A pro-p group-theoretic criterion for good reduction of ordinary proper hyperbolic curves (2017)
  • Author(s): 星裕一郎
  • Organizer: 2017 East Asian Core Doctorial Forum on Mathematics
  • Place of Presentation: 海外:ソウル(韓国)
  • Int'l Joint Research / Invited
• [Presentation] 巾零許容固有束の超特異因子について (2017)
  • Author(s): 星裕一郎
  • Organizer: 広島大学代数学セミナー
  • Place of Presentation: 国内:広島大学(広島県東広島市)
• [Presentation] 巾零許容固有束の超特異因子について (2017)
  • Author(s): 星裕一郎
  • Organizer: 東工大 数論・幾何学セミナー
  • Place of Presentation: 国内:東京工業大学(東京都目黒区)
• [Presentation] 絶対不分岐底上に安定還元を持つ曲線の等分点について (2016)
  • Author(s): 星裕一郎
  • Organizer: 大阪大学整数論&保型形式セミナー
  • Place of Presentation: 国内:大阪大学(大阪府豊中市)
  • Invited
• [Presentation] Introduction to Mono-anabelian Geometry I (2016)
  • Author(s): 星裕一郎
  • Organizer: Fundamental groups in arithmetic geometry - Paris 2016
  • Place of Presentation: 海外:パリ(フランス)
  • Int'l Joint Research / Invited
• [Presentation] Introduction to Mono-anabelian Geometry II (2016)
  • Author(s): 星裕一郎
  • Organizer: Fundamental groups in arithmetic geometry - Paris 2016
  • Place of Presentation: 海外:パリ(フランス)
  • Int'l Joint Research / Invited
• [Presentation] [IUTch-III-IV] from the point of view of mono-anabelian transport I (2016)
  • Author(s): 星裕一郎
  • Organizer: Inter-universal Teichmuller Theory Summit 2016
  • Place of Presentation: 国内:京都大学・数理解析研究所(京都府京都市)
  • Int'l Joint Research / Invited
• [Presentation] [IUTch-III-IV] from the point of view of mono-anabelian transport II (2016)
  • Author(s): 星裕一郎
  • Organizer: Inter-universal Teichmuller Theory Summit 2016
  • Place of Presentation: 国内:京都大学・数理解析研究所(京都府京都市)
  • Int'l Joint Research / Invited
• [Presentation] [IUTch-III-IV] from the point of view of mono-anabelian transport III (2016)
  • Author(s): 星裕一郎
  • Organizer: Inter-universal Teichmuller Theory Summit 2016
  • Place of Presentation: 国内:京都大学・数理解析研究所(京都府京都市)
  • Int'l Joint Research / Invited
• [Presentation] [IUTch-III-IV] from the point of view of mono-anabelian transport IV (2016)
  • Author(s): 星裕一郎
  • Organizer: Inter-universal Teichmuller Theory Summit 2016
  • Place of Presentation: 国内:京都大学・数理解析研究所(京都府京都市)
  • Int'l Joint Research / Invited
• [Presentation] Hodge-Arakelov-theoretic Evaluation I (2015)
  • Author(s): Yuichiro Hoshi
  • Organizer: Workshop on IUT theory of Shinichi Mochizuki
  • Place of Presentation: Oxford (UK)
  • Year and Date: 2015-12-10
  • Int'l Joint Research / Invited
• [Presentation] Hodge-Arakelov-theoretic Evaluation II (2015)
  • Author(s): Yuichiro Hoshi
  • Organizer: Workshop on IUT theory of Shinichi Mochizuki
  • Place of Presentation: Oxford (UK)
  • Year and Date: 2015-12-10
  • Int'l Joint Research / Invited
• [Presentation] An Approximate Statement of the Main Theorem of Inter-universal Teichmuller Theory (2015)
  • Author(s): Yuichiro Hoshi
  • Organizer: Workshop on IUT theory of Shinichi Mochizuki
  • Place of Presentation: Oxford (UK)
  • Year and Date: 2015-12-07
  • Int'l Joint Research / Invited
• [Presentation] Mono-anabelian Transport (2015)
  • Author(s): Yuichiro Hoshi
  • Organizer: Workshop on IUT theory of Shinichi Mochizuki
  • Place of Presentation: Oxford (UK)
  • Year and Date: 2015-12-07
  • Int'l Joint Research / Invited
• [Presentation] 宇宙際 Teichmuller 理論入門 III (2015)
  • Author(s): 星裕一郎
  • Organizer: 代数的整数論とその周辺 2015
  • Place of Presentation: 京都大学数理解析研究所（京都府京都市）
  • Year and Date: 2015-12-03
  • Invited
• [Presentation] 宇宙際 Teichmuller 理論入門 II (2015)
  • Author(s): 星裕一郎
  • Organizer: 代数的整数論とその周辺 2015
  • Place of Presentation: 京都大学数理解析研究所（京都府京都市）
  • Year and Date: 2015-12-02
  • Invited
• [Presentation] 宇宙際 Teichmuller 理論入門 I (2015)
  • Author(s): 星裕一郎
  • Organizer: 代数的整数論とその周辺 2015
  • Place of Presentation: 京都大学数理解析研究所（京都府京都市）
  • Year and Date: 2015-12-01
  • Invited
• [Presentation] Classical p-adic Teichmuller theory in characteristic three (2015)
  • Author(s): Yuichiro Hoshi
  • Organizer: AMS Summer Institute in Algebraic Geometry
  • Place of Presentation: Salt Lake City (USA)
  • Year and Date: 2015-07-30
  • Int'l Joint Research / Invited
• [Remarks] 星裕一郎＠京大数理研
  • URL: http://www.kurims.kyoto-u.ac.jp/~yuichiro/index.html
• [Remarks] Yuichiro HOSHI@RIMS
  • URL: http://www.kurims.kyoto-u.ac.jp/~yuichiro/index_e.html
• [Remarks] 星 裕一郎 の ホームページ
  • URL: http://www.kurims.kyoto-u.ac.jp/~yuichiro/index.html
• [Remarks] Yuichiro HOSHI's Home Page
  • URL: http://www.kurims.kyoto-u.ac.jp/~yuichiro/index_e.html
• [Funded Workshop] Inter-universal Teichmuller Theory Summit 2016 (2016)
  • Place of Presentation: 国内:京都大学・数理解析研究所(京都府京都市)
  • Year and Date: 2016-07-18