A research of algebraic cycles on local rings

• Project/Area Number: 18540052
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Meiji University
• Principal Investigator: KURANO Kazuhiko Meiji University, 理工学部, 教授 (90205188)
• Co-Investigator(Kenkyū-buntansha): KAMOI Yuji 明治大学, 商学部, 講師 (80308064) ; HAYASAKA Futoshi 明治大学, 理工学部, 講師 (20409460)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥630,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: グロタンディェク群 / チャウ群 / 代数サイクル / 代数学 / 局所環 / 代数的 K-理論 / 数値的同値 / Serre予想 / 交点数 / 完備匙 / Cox環 / トッド類 / 因子類群 / フロベニウス / デターミナント射 / 標準因子 / ヒルベルト・クンツ関数

Research Abstract

研究代表者はネーター局所環のチャウ群上で数値的同値を定義して、さらにその数値的同値で割った群は有限生成自由アーベル群になることを証明した。その理論をさらに発展させて局所環のチャウ群の構造を詳しく調べる。

Research Products

• [Journal Article] A local ring such that the map between Grothendieck groups with rational coefficients induced by completion is not injective (2008)
  • Author(s): K. Kurano and V. Srinivas
  • Journal Title: Michigan Math. J. 57 Pages: 485-498
  • Peer Reviewed
• [Journal Article] On vanishing of certain Ext modules (2008)
  • Author(s): S. Goto, F. Hayasaka and R. Takahashi
  • Journal Title: J. Math. Soc. Japan 60 Pages: 1045-1064
  • NAID: 10024905254
  • Peer Reviewed
• [Journal Article] A family of graded modules associated to a module (2008)
  • Author(s): F. Hayasaka and E. Hyry
  • Journal Title: Comm. Algebra 36 Pages: 4201-4217
  • Peer Reviewed
• [Journal Article] A loca1 ring such that the map between Grothendieck groups with rational coefficients induced by completion is not injedtive (2008)
  • Author(s): K. Kurano
  • Journal Title: Michigan Math. J. 57
  • Peer Reviewed
• [Journal Article] On vanishing of certain Ext modules (2008)
  • Author(s): S. Goto
  • Journal Title: J. Math. Soc. Japan 60
  • Peer Reviewed
• [Journal Article] A family of graded modules associated to a module (2008)
  • Author(s): F. Hayasaka
  • Journal Title: Comm. Algebra 36 Pages: 4201-4217
  • Peer Reviewed
• [Journal Article] The singular Riemann-Roch theorem and Hilbert-Kunz functions (2006)
  • Author(s): K. Kurano
  • Journal Title: J. Algebra 304 Pages: 487-499
  • Peer Reviewed
• [Journal Article] Asymptotic stability of primes associated to homogeneous components of multigraded modules (2006)
  • Author(s): F. Hayasaka
  • Journal Title: J. Algebra 306 Pages: 535-543
  • Peer Reviewed
• [Journal Article] The singular Riemann-Roch theorem and Hilbert-Kunz functions (2006)
  • Author(s): K.Kurano
  • Journal Title: J.Algebra 304
• [Journal Article] Asymptotic stability of primes associated to homogeneous components of multigraded modules (2006)
  • Author(s): F.Hayasaka
  • Journal Title: J.Algebra 306
• [Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities
  • Author(s): K. Kurano, E.-i. Sato, A. K. Singh and K.-i. Watanabe
  • Journal Title: J. of Algebra (掲載決定)
  • Peer Reviewed
• [Journal Article] 2変数Hilbert函数の多項式記述についての一考察
  • Author(s): 早坂太・山田修平
  • Journal Title: 明治大学理工学部研究報告 (掲載決定)
  • NAID: 40016269279
  • Peer Reviewed
• [Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities
  • Author(s): K. Kurano
  • Journal Title: J. of Algebra (to appear)(確定)
  • Peer Reviewed
• [Journal Article] 2変数Hilbert函数の多項式記述についての-考察
  • Author(s): 早坂太
  • Journal Title: 明治大学理工学部研究報告 (to appear)(確定)
  • Peer Reviewed
• [Journal Article] A local ring such・that the map between Grothendieck groups with rational coefficients induced by completion is not injective
  • Author(s): K.Kurano
  • Journal Title: Michigan Math.J (to appear)
  • Peer Reviewed
• [Journal Article] A family of graded modules associated to a module
  • Author(s): F.Hayasaka
  • Journal Title: Communications in Algebra (to appear)
  • Peer Reviewed
• [Presentation] パラメータ加群の重複度について (2009)
  • Author(s): 早坂太
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-29
• [Presentation] Nagata conjecture and symbolic Rees rings of space monomial curves (2009)
  • Author(s): K. Kurano
  • Organizer: The 4th Japan-Vietnam joint seminar on commutative algebra
  • Place of Presentation: 明治大学理工学部
  • Year and Date: 2009-02-21
• [Presentation] On the Buchsbaum-Rim multiplicity of a parameter module (2009)
  • Author(s): F. Hayasaka
  • Organizer: The 4-th Japan-Vietnam Joint Seminar on Commutative Algebra
  • Place of Presentation: 明治大学理工学部
  • Year and Date: 2009-02-21
• [Presentation] On the Buchsbaum-Rim multiplicity of a parameter module (2009)
  • Author(s): F. Hayasaka
  • Organizer: The 4-th Japan-Vietnam Joint Seminar on Comniutative Algebra
  • Place of Presentation: 明治大学理工学部
  • Year and Date: 2009-02-21
• [Presentation] ある素因子の集合の漸近挙動について (2009)
  • Author(s): 早坂太
  • Organizer: 第21回可換環論セミナー
  • Place of Presentation: 釧路市生涯学習センター
  • Year and Date: 2009-01-28
• [Presentation] 永田予想とspace monomial curveのsymbolic Rees代数について (2009)
  • Author(s): 藏野和彦
  • Organizer: 第21回可換環論セミナー
  • Place of Presentation: 釧路市生涯学習センター
  • Year and Date: 2009-01-27
• [Presentation] A note on Hilbert coefficients of Gorenstein graded rings (2009)
  • Author(s): 鴨井祐二
  • Organizer: 第21回可換環論セミナー
  • Place of Presentation: 釧路市生涯学習センター
  • Year and Date: 2009-01-27
• [Presentation] 永田予想と space monomial curve の symbolic Rees 代数について (2009)
  • Author(s): 蔵野和彦
  • Organizer: 第21回可換環論セミナー
  • Place of Presentation: 釧路市生涯学習センター
  • Year and Date: 2009-01-27
• [Presentation] A note on the Buchsbaum-Rim multiplicity (2008)
  • Author(s): 早坂太
  • Organizer: 第30回可換環論シンポジウム
  • Place of Presentation: 佐賀
  • Year and Date: 2008-11-18
• [Presentation] Gorenstein quotient isolated sigularities of odd prime dimension are cyclic (2008)
  • Author(s): K. Kurano
  • Organizer: COMMUTATIVE ALGEBRA AND ITS INTERACTION WITH ALGEBRAIC GEOMETRY
  • Place of Presentation: C.I.R.M. Luminy (France)
  • Year and Date: 2008-10-03
• [Presentation] Gorenstein quotient isolated sigularities of odd prime dimension are cyclic (2008)
  • Author(s): K. Kurano
  • Organizer: COMMUTATIVE ALGEBRA AND ITS INTERACTION WITH ALGEBRAIC GEOMETRY
  • Place of Presentation: C. I. R. M. Luminy (France)
  • Year and Date: 2008-10-03
• [Presentation] Symbolic Rees rings of space monomial curves in characteristic p and existence of negative curves in characteristic 0 (2008)
  • Author(s): K. Kurano
  • Organizer: INTERNATIONAL CONFERENCE "Towards establishing a cutting-edge platform for commutative ring theory in the 21th century
  • Place of Presentation: 横浜開港記念会館
  • Year and Date: 2008-03-20
• [Presentation] Symbohc Reesrings of space monomial curves in charactehstic $P$ and existence of negative curves in characteristic $0$ (2008)
  • Author(s): 藏野 和彦
  • Organizer: INTERNATIONAL CONFERENCE "Towards estabhshing a cutting-edge platfom for commnutative ring theory in the 21th eentury"
  • Place of Presentation: 横浜開講記念会館
  • Year and Date: 2008-03-20
• [Presentation] Hard Lefschetz theorem and standard conjecture in commutative ring theory (2008)
  • Author(s): 藏野和彦
  • Organizer: ミニ研究集会釧路2008
  • Place of Presentation: 北海道教育大学釧路校
  • Year and Date: 2008-02-18
• [Presentation] Hard Lefschetz theorem and standard eonjecture in commutative ringtheory (2008)
  • Author(s): 藏野 和彦
  • Organizer: ミニ研究集会釧路2008
  • Place of Presentation: 北海道教育大学釧路校
  • Year and Date: 2008-02-18
• [Presentation] Aパラメータ加群とブックスバウム・リム重複度 (2008)
  • Author(s): 早坂 太
  • Organizer: 第20回可換環論セミナー
  • Place of Presentation: 千葉県勝浦市
  • Year and Date: 2008-01-30
• [Presentation] パラメータ加群とブックスバウム・リム重複度 (2008)
  • Author(s): 早坂太
  • Organizer: 第20回可換環論セミナー
  • Place of Presentation: 千葉
  • Year and Date: 2008-01-28
• [Presentation] A family of graded modules associated tO a module (2008)
  • Author(s): 早坂 太
  • Organizer: International Conferance in Commutative Algebra
  • Place of Presentation: IIT-Bombay、インド
  • Year and Date: 2008-01-10
• [Presentation] A family of graded modules associated to a module (2008)
  • Author(s): F. Hayasaka
  • Organizer: International Conference in Commutative Algebra, IIT-Bombay
  • Place of Presentation: Mumbai(India)
  • Year and Date: 2008-01-08
• [Presentation] A local ring such that the map between Grothendieck group with rational coefficients induced by completion is not injective (2007)
  • Author(s): K. Kurano
  • Organizer: The 3rd Japan-Vietnam joint seminar on commutative algebra
  • Place of Presentation: Institute of Mathematics, Hanoi, Vietnam
  • Year and Date: 2007-12-05
• [Presentation] A local suchthat the map between Grothendieck groupwith rational coeffcients induced by completion is not injective (2007)
  • Author(s): 藏野 和彦
  • Organizer: The 3rd Japan-Vietnam joint seminar on commutative algebra
  • Place of Presentation: Institute of Mathematics,Hanoi,Vietnam
  • Year and Date: 2007-12-05
• [Presentation] On certain graded modules associated to a module (2007)
  • Author(s): 早坂 太
  • Organizer: The 3rd Japan-Vietnam joint seminar on commutative algebra
  • Place of Presentation: InStit,ut,e of Mathematics,Hanoi,Vietnam
  • Year and Date: 2007-12-04
• [Presentation] On certain graded modules associated to a module (2007)
  • Author(s): F. Hayasaka
  • Organizer: The 3rd Japan-Vietnam Joint Seminar on Commutative Algebra
  • Place of Presentation: Institute of Mathematics, Hanoi, Vietnam
  • Year and Date: 2007-12-03
• [Presentation] Symbolic Rees rings of space monomial curves in characteristic p and existence of negative curves in characteristic 0 (2007)
  • Author(s): 藏野和彦
  • Organizer: 第29回可換環論シンポジウム
  • Place of Presentation: 愛知厚生年金会館ウェルシティなごや
  • Year and Date: 2007-11-21
• [Presentation] Symbolic Rees rings of space monomial curves in characteristic $p$ and existence of neaeive curves in eharacteristic $0$ (2007)
  • Author(s): 藏野 和彦
  • Organizer: 第29回可換環論シンポジウム
  • Place of Presentation: 愛知厚生年金会館ウェルシティなごや
  • Year and Date: 2007-11-21
• [Presentation] A family of graded modules associated to a module (2007)
  • Author(s): 早坂太
  • Organizer: 第29回可換環論シンポジウム
  • Place of Presentation: 愛知厚生年金会館ウェルシティなごや
  • Year and Date: 2007-11-19
• [Presentation] 加群に随伴するある次数加群の族について (2007)
  • Author(s): 早坂太
  • Organizer: 日本数学会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-23
• [Presentation] Intersection multiplicity の代数的記述について (2007)
  • Author(s): 藏野和彦
  • Organizer: 第52回代数学シンポジウム
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-08-09
• [Presentation] Intersection muhphcity の代数的記述について (2007)
  • Author(s): 藏野 和彦
  • Organizer: 第52回代数学シンポジウム
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-08-09
• [Presentation] An example of a local ring R such that G_0(R)_Q-> G_0(R^)_Q is not injective (2007)
  • Author(s): K. Kurano
  • Organizer: Commutative Algebra and its Interaction with Algebraic Geometry
  • Place of Presentation: BIRS (Banff International Research Station), カナダ
  • Year and Date: 2007-06-14
• [Presentation] An example of a local ring R such that.G_0(R)_Q->G_0(R^)_Q is not inject.ive (2007)
  • Author(s): 藏野 和彦
  • Organizer: Gommutative Algebra and its Interaction with Alebraic Geometry
  • Place of Presentation: BIRS,カナダ
  • Year and Date: 2007-06-14
• [Presentation] Intersection multiplicityの代数的な記述について (2007)
  • Author(s): 藏野和彦
  • Organizer: 第2回代数・解析・幾何学セミナー
  • Place of Presentation: 鹿児島大学理学部
  • Year and Date: 2007-02-19
• [Presentation] A certain family of graded modules associated to a module (2007)
  • Author(s): 早坂太
  • Organizer: 第19回可換環論セミナー
  • Place of Presentation: 九州大学
  • Year and Date: 2007-01-29
• [Presentation] Symbolic Rees環(ある正規射影局面の全座標環)の有限生成性-MATLABを使った計算実験- (2007)
  • Author(s): 藏野和彦
  • Organizer: 計算可換代数と計算代数幾何
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2007-01-18
• [Presentation] An example of a local ring A such that the kernel of the map from {\rm G}_0(A)to {\rm G}_0(\hat{A})is not torsion (2006)
  • Author(s): 藏野和彦
  • Organizer: 第28回可換環論シンポジウム
  • Place of Presentation: ウェルサンピア多摩
  • Year and Date: 2006-11-16
• [Presentation] On the algebraic description of intersection multiplicity due to Serre (2006)
  • Author(s): 藏野和彦
  • Organizer: 第二回モチーフ勉強会
  • Place of Presentation: 東大数理
  • Year and Date: 2006-09-29
• [Presentation] Numerical equivalence and the vanishing conjecture (2006)
  • Author(s): K. Kurano
  • Organizer: Homological Conjectures in Commutative Algebra, A Conference in Honor of Paul Roberts' 60th Birthday
  • Place of Presentation: Snowbird, Utah アメリカ合衆国
  • Year and Date: 2006-05-19
• [Remarks]
  • URL: http://www.math.meiji.ac.jp/~kurano/