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

Published electronically:
November 1, 2007

MathSciNet review:
2358489

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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**, 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**, 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**, 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****[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****[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**, 10.1007/BF01420335

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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

Received by editor(s):
January 16, 2007

Received by editor(s) in revised form:
February 5, 2007

Published electronically:
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.