Arithmetic geometry through higher dimensional class field theory

• Project/Area Number: 21740015
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hiroshima University
• Principal Investigator: HIRANOUCHI Toshiro 広島大学, 大学院・理学研究科, 助教 (30532551)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); 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: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 高次元類体論 / 代数的 K 理論 / 代数的K理論 / 分岐理論

Research Abstract

We have obtained the following results:
1. The structure of the Milnor K-group of a mixed characteristic complete discrete valuation field
2. Calculation of the image of the cycle map and the Chow group of the product of elliptic curves over p-adic field
3. Definition of the Milnor type K-group attached to commutative algebraic groups and its applications

Research Products

• [Journal Article] On the cycle map for products of elliptic curves over a p-adic field (2013)
  • Author(s): T. Hiranouchi and S. Hirayama
  • Journal Title: Acta Arith Volume: 157 Issue: 2 Pages: 101-118
  • DOI: 10.4064/aa157-2-1
  • Peer Reviewed
• [Journal Article] Milnor K-groups modulo pn of a complete discrete valuation field (2012)
  • Author(s): T.Hiranouchi
  • Journal Title: Proceedings of the Japan Academy, Series A Volume: 88 Issue: 4 Pages: 59-61
  • DOI: 10.3792/pjaa.88.59
  • Peer Reviewed
• [Journal Article] Milnor K-groups modulo p^n of a complete discrete valuation field (2012)
  • Author(s): 平之内俊郎
  • Journal Title: Proc.Japan Acad., Ser.A Volume: (掲載決定)
  • Peer Reviewed
• [Journal Article] Flat Modules and Groebner Bases over Truncated Discrete Valuation Rings (2010)
  • Author(s): Toshiro Hiranouchi, Yuichiro Taguchi
  • Journal Title: Interdisciplinary Information Sciences Volume: 16 Issue: 1 Pages: 33-37
  • DOI: 10.4036/iis.2010.33
  • NAID: 110009794871
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed
• [Journal Article] Class field theory for open curves over p-adic fields (2010)
  • Author(s): T. Hiranouchi
  • Journal Title: Math. Z. Volume: 266、no.1 Issue: 1 Pages: 107-113
  • DOI: 10.1007/s00209-009-0556-1
  • Peer Reviewed
• [Journal Article] Pure weight perfect Modules on divisorial schemes (2010)
  • Author(s): T. Hiranouchi and S. Mochizuki
  • Journal Title: in ``Deformation Spaces'', Edited by: Hossein Abbaspour, Universit￥'e de Nantes, France, Matilde Marcolli, California Institute of Technology, Pasadena, CA, and Thomas Tradler, New York City College of Technology (CUNY), NY A publication of Vieweg Verlag Volume: 129,no. 11 Pages: 2702-2712
  • DOI: 10.1007/978-3-8348-9680-3_3
  • ISBN: 9783834812711, 9783834896803
  • Peer Reviewed
• [Journal Article] Ramification theory of truncated discrete valuation rings : a survey (2010)
  • Author(s): 平之内俊郎
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B19 Pages: 35-43
  • Peer Reviewed
• [Journal Article] Flat modules and Groebner bases over truncated discrete valuation rings (2010)
  • Author(s): 平之内俊郎・田口雄一郎
  • Journal Title: Interdisciplinary of Information Sciences (IIS) Volume: 16 Pages: 33-37
  • NAID: 110009794871
  • Peer Reviewed
• [Journal Article] Class field theory for open curves over p-adic fields (2010)
  • Author(s): 平之内俊郎
  • Journal Title: Math.Z. Volume: 266 Pages: 107-113
  • Peer Reviewed
• [Journal Article] Pure weight perfect Modules on divisorial schemes (2010)
  • Author(s): 平之内俊郎・望月哲史
  • Journal Title: "Deformation Spaces", Edited by : Hossein Abbaspour and Thomas Tradler, Aspects Math. Volume: E40 Pages: 75-89
  • Peer Reviewed
• [Journal Article] Smallness of fundamental groups for arithmetic schemes (2009)
  • Author(s): 原田新也, 平之内俊郎
  • Journal Title: J.Number Theory 129 Pages: 2702-2712
  • Peer Reviewed
• [Journal Article] Pure weight perfect Modules on divisorial schemes
  • Author(s): 望月哲史, 平之内俊郎
  • Journal Title: Aspects Math. (掲載決定)
  • Peer Reviewed
• [Journal Article] Class field theory for open curves over p-adic fields
  • Author(s): 平之内俊郎
  • Journal Title: Math. Z. (掲載決定)
  • Peer Reviewed
• [Journal Article] Flat modules and Groebner bases over truncated discrete valuation rings
  • Author(s): 平之内俊郎, 田口雄一郎
  • Journal Title: Interdisciplinary of Information Sciences (掲載決定)
  • NAID: 110009794871
  • Peer Reviewed
• [Journal Article] Ramification theory of truncated discrete valuation rings : a survey
  • Author(s): 平之内俊郎
  • Journal Title: "Algebraic Number Theory and Related Topics 2008" -a volume in RIMS-Bessatsu Series- (掲載決定)
  • Peer Reviewed
• [Presentation] A tensor product in the category of reciprocity functors (2013)
  • Author(s): 平之内俊郎
  • Organizer: KANT2013
  • Place of Presentation: 九州大学
  • Year and Date: 2013-02-11
• [Presentation] A tensor product in the category of reciprocity functors (2013)
  • Author(s): 平之内俊郎
  • Organizer: 九州代数的整数論 2013
  • Place of Presentation: 九州大学
  • Invited
• [Presentation] 代数群に付随する Milnor 型K群と加法的 Chow 群, 代数的整数論とその周辺 (2012)
  • Author(s): 平之内俊郎
  • Organizer: 京都大学数理解析研究所
  • Year and Date: 2012-12-06
• [Presentation] Bloch-加藤予想の楕円曲線類似について (2012)
  • Author(s): 平之内俊郎
  • Organizer: 大阪大学整数論&保型形式セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2012-11-30
• [Presentation] Kahler微分と染川K群, KANT2012 (2012)
  • Author(s): 平之内俊郎
  • Organizer: 九州大学
  • Year and Date: 2012-02-23
• [Presentation] 染川K群とKahler微分 (2012)
  • Author(s): 平之内俊郎
  • Organizer: KANT2012
  • Place of Presentation: 九州大学(招待講演)
  • Year and Date: 2012-02-23
• [Presentation] Milnor K-group of a complete discrete valuation field (2012)
  • Author(s): 平之内俊郎
  • Organizer: 日本数学会中四国例会
  • Place of Presentation: 岡山大学
  • Year and Date: 2012-01-22
• [Presentation] 代数群に付随するMilnor 型K 群と加法的Chow 群 (2012)
  • Author(s): 平之内俊郎
  • 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
  • Invited
• [Presentation] On the image of the cycle map for the product of elliptic curves over a p-adic feld (2011)
  • Author(s): 平之内俊郎
  • Organizer: Industrious number theory 3, Korea Institute for Advanced Study
  • Place of Presentation: Korea
  • Year and Date: 2011-11-12
• [Presentation] non-connected K-theory revisited (2011)
  • Author(s): 平之内俊郎
  • Organizer: algebra seminar, KIAS
  • Place of Presentation: Korea
  • Year and Date: 2011-09-08
• [Presentation] ∞-categories for the working mathematician (2011)
  • Author(s): 平之内俊郎
  • Organizer: algebra seminar, KIAS
  • Place of Presentation: Korea
  • Year and Date: 2011-09-07
• [Presentation] ∞圏の圏のモデルについて (2011)
  • Author(s): 平之内俊郎
  • Organizer: SGAD2011
  • Place of Presentation: 京都大学
  • Year and Date: 2011-04-12
• [Presentation] ∞-categories for the working mathematician (2011)
  • Author(s): 平之内俊郎
  • Organizer: SGAD2011
  • Place of Presentation: 京都大学
  • Year and Date: 2011-04-12
• [Presentation] presentable(∞)圏と∞トポス (2011)
  • Author(s): 平之内俊郎
  • Organizer: SGAD2011
  • Place of Presentation: 京都大学
  • Year and Date: 2011-04-12
• [Presentation] On a filtration of Milnor K-groups modulo p^n for a henselian discrete valuation field (2011)
  • Author(s): 平之内俊郎
  • Organizer: KANT2011
  • Place of Presentation: 九州大学
  • Year and Date: 2011-02-18
• [Presentation] On a filtration of Milnor K-groups modulo p^n for a henselian discrete valuation field (2011)
  • Author(s): 平之内俊郎
  • Organizer: KANT2011
  • Place of Presentation: 福岡・九州大学(招待講演)
  • Year and Date: 2011-02-18
• [Presentation] On the image of the cycle map for the product of elliptic curves over a p-adic feld (2010)
  • Author(s): 平之内俊郎
  • Organizer: Industrious number theory 3
  • Place of Presentation: 韓国・ソウル・KIAS(招待講演)
  • Year and Date: 2010-11-12
• [Presentation] On the image of the cycle map for the product of elliptic curves over a p-adic feld (2010)
  • Author(s): 平之内俊郎
  • Organizer: Oberseminar
  • Place of Presentation: Essen-Duisburg 大 学 , Germany
  • Year and Date: 2010-10-14
• [Presentation] On a filtration associated with an isogeny on formal groups (2010)
  • Author(s): 平之内俊郎
  • Organizer: 第9回仙台広島整数論集
  • Place of Presentation: 東北大学
  • Year and Date: 2010-07-20
• [Presentation] On a filtration associated with an isogeny on formal groups (2010)
  • Author(s): 平之内俊郎
  • Organizer: 第9回仙台広島整数論集会
  • Place of Presentation: 仙台・東北大学(招待講演)
  • Year and Date: 2010-07-20
• [Presentation] Quasi-weak equivalences in complicial exact categories (2010)
  • Author(s): 平之内俊郎
  • Organizer: 九州大学代数学セミナー
  • Place of Presentation: 九州大学
  • Year and Date: 2010-02-19
• [Presentation] Quasi-weak equivalences in complicial exact categories (2010)
  • Author(s): 平之内俊郎
  • Organizer: Sakura Workshop "Torsion of abelian schemes and rational points on moduli spaces",IMB
  • Place of Presentation: France
  • Year and Date: 2010-01-29
• [Presentation] Quasi-weak equivalences in complicial exact categories (2010)
  • Author(s): 平之内俊郎
  • Organizer: Sakura Workshop "Torsion of abelian schemes and rational points on moduli spaces"
  • Place of Presentation: フランス・ボルドー
  • Year and Date: 2010-01-29
• [Presentation] 非連結 K 群について (2010)
  • Author(s): 平之内俊郎
  • Organizer: 九州代数的整数論2010
  • Place of Presentation: 九州大学
• [Presentation] 最近の高次元類体論について (2009)
  • Author(s): 平之内俊郎
  • Organizer: 広島大学理学研究科数学教室談話会
  • Place of Presentation: 広島大学
  • Year and Date: 2009-12-01
• [Presentation] Smallness of fundamental groups for varieties over finite fields t-motives: Hodge structures (2009)
  • Author(s): 平之内俊郎
  • Organizer: transcendence and other motivic aspects, BIRS
  • Place of Presentation: Canada
  • Year and Date: 2009-10-01
• [Presentation] Smallness of fundamental groups for varieties over finite fields (2009)
  • Author(s): 平之内俊郎
  • Organizer: t-motives : Hodge structures, transcendence and ot her motivic aspects
  • Place of Presentation: カナダ・バンフ
  • Year and Date: 2009-10-01
• [Presentation] Pure weight perfect Modules on divisorial schemes (2009)
  • Author(s): 平之内俊郎
  • Organizer: 第8回広島整数論集会
  • Place of Presentation: 広島大学
  • Year and Date: 2009-07-24
• [Presentation] Pure weight perfect Modules on divisorial schemes (2009)
  • Author(s): 平之内俊郎
  • Organizer: 第8回広島整数論集会
  • Place of Presentation: 東広島市
  • Year and Date: 2009-07-24
• [Presentation] 最近の高次元類体論について (2009)
  • Author(s): 平之内俊郎
  • Organizer: 京都大学数理解析研究所談話会
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-06-17