algebraic cobordism and motivic cohomology

• Project/Area Number: 20540061
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Ibaraki University
• Principal Investigator: YAGITA Nobuaki 茨城大学, 教育学部, 教授 (20130768)
• Co-Investigator(Kenkyū-buntansha): OKAYASU Takashi 茨城大学, 教育学部, 教授 (00191958) ; KUDOU Kenji 茨城大学, 教育学部, 講師 (00114017)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); 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: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 代数的同境界理論 / モチビックコホモロジー / 分類空間 / BP-理論

Research Abstract

Firstly, by using geometric arguments, we compute algebraic cobordism, next we compute motivic cohomology using fields theories. The concrete spaces which we can compute are classifying spaces, for example, BU(n), BO(n) and quadrics, in particular over the real number field.

Research Products

• [Journal Article] Note on Chow rings of nontrivial G-torsors over a field (2011)
  • Author(s): N. Yagita
  • Journal Title: Kodai Math. J. Volume: 34 Pages: 446-463
  • NAID: 130004687959
  • Peer Reviewed
• [Journal Article] The image of the map from group cohomology to Galois cohomology (2011)
  • Author(s): M. Tezuka and N. Yagita
  • Journal Title: Trans. AMS Volume: 363 Pages: 4475-4503
  • Peer Reviewed
• [Journal Article] The image of the map from group cohomology to Galois cohomology (2011)
  • Author(s): M.Tezuka, N.Yagita
  • Journal Title: Trans.Amer.Math.Soc. Volume: 363 Pages: 4475-4503
  • Peer Reviewed
• [Journal Article] Note on Chow rings of nontrivial G-torsor over a field (2011)
  • Author(s): N.Yagita
  • Journal Title: Kodai Math.J. Volume: 34 Pages: 446-463
  • NAID: 130004687959
  • Peer Reviewed
• [Journal Article] Coniveau filtration of cohomology of groups (2010)
  • Author(s): N. Yagita
  • Journal Title: Proc. London Math. Soc. Volume: 101 Pages: 179-206
  • Peer Reviewed
• [Journal Article] Motivic cohomology of quadratic and the coniveau spectral sequence (2010)
  • Author(s): N. Yagita
  • Journal Title: J. K-theory Volume: 6 Pages: 547-589
  • Peer Reviewed
• [Journal Article] The complex cordism of BSO_n (2010)
  • Author(s): K. Inoue and N. Yagita
  • Journal Title: Kyoto J. Math Volume: 50 Pages: 307-324
  • Peer Reviewed
• [Journal Article] Chern subrings (2010)
  • Author(s): M. Kameko and N. Yagita
  • Journal Title: Proc. AMS Volume: 138 Pages: 367-373
  • Peer Reviewed
• [Journal Article] New examples of hyper surface with constant positive scalar curvature in the Euclidean space (2010)
  • Author(s): T. Okayasu
  • Journal Title: J. Math Soc. Japan Pages: 1137-1166
  • Peer Reviewed
• [Journal Article] Chow subring. (2010)
  • Author(s): M.Kameko, N.Yagaita
  • Journal Title: Proc.Amer.Math.Soc. 15 Pages: 367-373
  • Peer Reviewed
• [Journal Article] Coniveau filtration of groups. (2010)
  • Author(s): N.Yagita
  • Journal Title: Proc.London Math.Soc. 101 Pages: 179-206
  • Peer Reviewed
• [Journal Article] Motivic cohomology of quadrics and the coniveau spectral sequence. (2010)
  • Author(s): N.Yagita
  • Journal Title: J.K-theory 6 Pages: 547-589
  • Peer Reviewed
• [Journal Article] Chern subrings (2010)
  • Author(s): M.Kameko, N.Yagita
  • Journal Title: Prom.Amer.Math.Soc. Volume: 13 Pages: 367-373
  • Peer Reviewed
• [Journal Article] Coniveau filtrations of groups (2010)
  • Author(s): N.Yagita
  • Journal Title: Proc.London Math.Soc. Volume: 101 Pages: 179-206
  • Peer Reviewed
• [Journal Article] Motivic cohomology of quadrics and coniveau spectral sequence (2010)
  • Author(s): N.Yagita
  • Journal Title: J.of K-theory Volume: 3 Pages: 574-589
  • Peer Reviewed
• [Journal Article] Chern subrings (2010)
  • Author(s): M.Kameko, N.Yagita
  • Journal Title: Procc. Amer. Math. Soc 13 Pages: 367-373
  • Peer Reviewed
• [Journal Article] Chow rings of excellent quadrics (2008)
  • Author(s): N. Yagita
  • Journal Title: J. Pure and Appl. Algebra. Volume: 212 Pages: 2440-2449
  • Peer Reviewed
• [Journal Article] The Brown-Peterson cohomology of the classifying spaces of projective unitary group PU(p) and the exceptional Lie groups (2008)
  • Author(s): M. Kameko and N. Yagita
  • Journal Title: Trans. AMS Volume: 360 Pages: 2265-2284
  • Peer Reviewed
• [Journal Article] Chow rings of excellent quadrics (2008)
  • Author(s): N. Yagita
  • Journal Title: J. Pure Appl. Algebra. 212 Pages: 2440-2449
  • Peer Reviewed
• [Journal Article] The Brown-Peterson cohomology of classifying spaces of the projective unitary groups PU (p) and exceptional Lie groups (2008)
  • Author(s): M. Kameko and N.Yagita
  • Journal Title: Trans. of Amer. Math. Soc 360 Pages: 2267-2284
  • Peer Reviewed
• [Journal Article] Coniveau filtrations of groups
  • Author(s): N.Yagita
  • Journal Title: Proc.London Math. Soc. (掲載予定) Pages: 2010-2010
  • Peer Reviewed
• [Remarks]
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• [Remarks]
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• [Remarks] 茨城大学研究者情報総覧
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