DOI QR코드

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STABLE CLASS OF EQUIVARIANT ALGEBRAIC VECTOR BUNDLES OVER REPRESENTATIONS

  • 발행 : 2002.05.01

초록

Let G be a reductive algebraic group and let B, F be G-modules. We denote by $VEC_{G}$ (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that $VEC_{G}$ (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor $VEC_{G}$ (B, $F^{\chi}$) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.

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참고문헌

  1. Introduction to Commutative Algebra M. Atiyah;I. Macdonald
  2. Amer. Math. Soc. Algebraic group actions on office spaces, Group actions on rings H. Bass.
  3. Trans. Amer. Math. Soc. v.292 Linearizing certain reductive group actions H. Bass;W. Haboush https://doi.org/10.2307/2000224
  4. Comm. Algebra v.15 Some equiuariant K-theory of addine algebraic group actions https://doi.org/10.1080/00927878708823417
  5. Invent. Math. v.119 An equivariant version of Grauert's Oka principle P. Heinzner;F. Kutzschbauch https://doi.org/10.1007/BF01245185
  6. Invent. Math. v.105 Nichtlinearisierbare Operationen halbeinfacher Gruppen auf affinen Raumen F. Kmop https://doi.org/10.1007/BF01232264
  7. Proceedings of the Conference on Group Actions and Invariant Theory, Montreal 1988, CMS Conference Proceedings v.10 G-vector bundles and the linearization problem H. Kraft
  8. Inst. Hautes Etudes Sci. Publ. Math. v.76 Reductive group actions with one dimensional quotient H. Kraft;G. Schwarz https://doi.org/10.1007/BF02699430
  9. GTM 131 A First Course in Noncommutative Rings T. Y. Lam.
  10. Bull. Soc. Math. France, Paris, Memoire v.33 Slices Etales D. Luna
  11. Duke Math. J. v.88 Moduli of equivariant algebraic vector bundles over a product of affine varieties K. Masuda https://doi.org/10.1215/S0012-7094-97-08806-2
  12. Current Trends in Transformation Groups, K-Monographs in Mathematics Equivariant algebraic vector bundles over representations - a survey
  13. Proc. Nat. Acad. Sci. U.S.A. v.88 Equivariant algebraic vector bundles over representations of reductive groups;Applications M. Masuda;L. Moser-Jauslin;T. Petrie https://doi.org/10.1073/pnas.88.20.9065
  14. Topology v.35 The equivariant Serre problem for abelian groups https://doi.org/10.1016/0040-9383(95)00026-7
  15. Topology v.37 Invariants of equivariant algebraic vector bundles and inequalities for dominant weights https://doi.org/10.1016/S0040-9383(97)00017-7
  16. Proc. Nat. Acad. Sci. U.S.A. v.88 Equivariant algebraic vector bundles over representations of reductive groups;Theory M. Masuda;T. Petrie https://doi.org/10.1073/pnas.88.20.9061
  17. J. Amer. Math. Soc. v.8 Stably trivial equivariant algebraic vector bundles https://doi.org/10.2307/2152927
  18. Invent. Math. v.36 Projective modules over polynomial rings D. Quillen https://doi.org/10.1007/BF01390008
  19. C. R. Acad. Sci. Paris v.309 Exotic algebraic group actions G. Schwarz
  20. Topological methods in algebraic transformation groups, Progress in Math. v.80 The topology of algebraic quotients
  21. Dokl. Acad. Nauk SSSR v.26 Projective modules over a polynomial rings A. Suslin