Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The BGQ spectral sequence for noncommutative spaces

Author: Christopher J. Pappacena
Journal: Proc. Amer. Math. Soc. 132 (2004), 633-639
MSC (2000): Primary 18E15, 19D10; Secondary 14A22, 16P40, 16W50, 19D50
Published electronically: October 8, 2003
MathSciNet review: 2019937
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove an analogue of the Brown-Gersten-Quillen (BGQ) spectral sequence for noncommutative spaces. As applications, we consider this spectral sequence over affine and projective spaces associated to right fully bounded noetherian (FBN) rings.

References [Enhancements On Off] (What's this?)

  • 1. M. Artin and J. Zhang, Noncommutative projective schemes, Adv. Math. 109 (1994), 228-287. MR 96a:14004
  • 2. P. Gabriel, Des catégories abéliennes, Bull. Math. Soc. France 90 (1962), 323-448. MR 38:1144
  • 3. K. Goodearl and R. Warfield, An Introduction to Noncommutative Noetherian Rings, London Mathematical Society Student Texts 16, Cambridge University Press, Cambridge, 1989. MR 91c:16001
  • 4. K. Goodearl and J. T. Stafford, The graded verson of Goldie's Theorem, Contemporary Mathematics 259 (2000), 237-240. MR 2001g:16087
  • 5. R. Gordon and J. C. Robson, Krull dimension, Memoirs Amer. Math. Soc. 133, 1973. MR 50:4664
  • 6. C. Nastacescu and F. Van Ostayen, Graded Ring Theory, North-Holland, Amsterdam, 1982. MR 84i:16002
  • 7. C. J. Pappacena, The injective spectrum of a noncommutative space, J. Algebra 250 (2002), 559-602. MR 2003d:16007
  • 8. D. Quillen, Higher algebraic K-theory I, Algebraic $K$-Theory, Batelle, 1972 (H. Bass, ed.) Lecture Notes in Mathematics 341, Springer-Verlag, Berlin, 1973, 85-147. MR 49:2895
  • 9. S. P. Smith, Subspaces of non-commutative spaces, Trans. Amer. Math. Soc. 354 (2002), 2131-2171. MR 2003f:14002
  • 10. M. Van den Bergh, Blowing up of non-commutative smooth surfaces, Memoirs Amer. Math. Soc. 154, no. 734, 2001. MR 2002k:16057

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 18E15, 19D10, 14A22, 16P40, 16W50, 19D50

Retrieve articles in all journals with MSC (2000): 18E15, 19D10, 14A22, 16P40, 16W50, 19D50

Additional Information

Christopher J. Pappacena
Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798
Email: Chris_\,

Keywords: BGQ spectral sequence, noncommutative geometry, right FBN ring
Received by editor(s): August 18, 2002
Published electronically: October 8, 2003
Additional Notes: The author was partially supported by a postdoctoral fellowhip from the Mathematical Sciences Research Institute, a summer sabbatical from Baylor University, and a grant from the National Security Agency.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society