|
Global coefficient ring in the Nilpotence Conjecture
Author:
Joseph Gubeladze
Journal:
Proc. Amer. Math. Soc. 136 (2008), 499-503
MSC (2000):
Primary 19D50; Secondary 13B40, 13K05, 20M25
Posted:
November 1, 2007
MathSciNet review:
2358489
Full-text PDF
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this note we show that the nilpotence conjecture for toric varieties is true over any regular coefficient ring containing  .
- [BG]
W. Bruns and J. Gubeladze, Polytopes, Rings, and
 -theory, book in preparation. (Preliminary version: http://math.sfsu.edu/gubeladze/publications/kripo.html)
- [G]
Joseph
Gubeladze, The nilpotence conjecture in 𝐾-theory of toric
varieties, Invent. Math. 160 (2005), no. 1,
173–216. MR 2129712
(2006d:14057), http://dx.doi.org/10.1007/s00222-004-0410-3
- [K]
Wilberd
van der Kallen, Descent for the 𝐾-theory of polynomial
rings, Math. Z. 191 (1986), no. 3,
405–415. MR
824442 (87h:13012), http://dx.doi.org/10.1007/BF01162716
- [L]
Hartmut
Lindel, On the Bass-Quillen conjecture concerning projective
modules over polynomial rings, Invent. Math. 65
(1981/82), no. 2, 319–323. MR 641133
(83g:13009), http://dx.doi.org/10.1007/BF01389017
- [St]
Jan
Stienstra, Operations in the higher 𝐾-theory of
endomorphisms, Current trends in algebraic topology, Part 1 (London,
Ont., 1981) CMS Conf. Proc., vol. 2, Amer. Math. Soc., Providence,
R.I., 1982, pp. 59–115. MR 686113
(84d:14012)
- [Sw]
Richard
G. Swan, Néron-Popescu desingularization, Algebra and
geometry (Taipei, 1995) Lect. Algebra Geom., vol. 2, Int. Press,
Cambridge, MA, 1998, pp. 135–192. MR 1697953
(2000h:13006)
- [V]
Ton
Vorst, Localization of the 𝐾-theory of polynomial
extensions, Math. Ann. 244 (1979), no. 1,
33–53. With an appendix by Wilberd van der Kallen. MR 550060
(80k:18016), http://dx.doi.org/10.1007/BF01420335
- [BG]
- W. Bruns and J. Gubeladze, Polytopes, Rings, and -theory, book in preparation. (Preliminary version: http://math.sfsu.edu/gubeladze/publications/kripo.html)
- [G]
- J. Gubeladze, The nilpotence conjecture in
 -theory of toric varieties, Invent. Math. 160 (2005), 173-216. MR 2129712 (2006d:145057)
- [K]
- W. van der Kallen, Descent for the K-theory of polynomial rings, Math. Z. 191 (1986), 405-415. MR 0824442 (87h:13012)
- [L]
- H. Lindel, On the Bass-Quillen conjecture concerning projective modules over polynomial rings, Invent. Math. 65 (1981), 319-323. MR 0641133 (83g:13009)
- [St]
- J. Stienstra, Operations in the higher K-theory of endomorphisms. (Current trends in algebraic topology, Part 1, Semin. London/Ont. 1981), CMS Conf. Proc. 2, Amer. Math. Soc., Providence, R.I., 1982, 59-115. MR 0686113 (84d:14012)
- [Sw]
- R. Swan, Néron-Popescu desingularization, in Algebra and Geometry, 135-192, Lect. Algebra Geom. 2, Internat. Press, Cambridge, MA, 1998. MR 1697953 (2000h:13006)
- [V]
- T. Vorst, Localization of the
 -theory of polynomial extensions, Math. Ann. 244 (1979), 33-53. MR 0550060 (80k:18016)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2000):
19D50,
13B40,
13K05,
20M25
Retrieve articles in all journals
with MSC (2000):
19D50,
13B40,
13K05,
20M25
Additional Information
Joseph Gubeladze
Affiliation:
Department of Mathematics, San Francisco State University, San Francisco, California 94132
Email:
soso@math.sfsu.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-07-09106-X
PII:
S 0002-9939(07)09106-X
Received by editor(s):
January 16, 2007
Received by editor(s) in revised form:
February 5, 2007
Posted:
November 1, 2007
Additional Notes:
The author was supported by NSF grant DMS-0600929
Communicated by:
Martin Lorenz
Article copyright:
© Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
|
