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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Global coefficient ring in the Nilpotence Conjecture

Author(s): 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
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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 $ \mathbb{Q}$.

References:

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W. Bruns and J. Gubeladze, Polytopes, Rings, and $ K$-theory, book in preparation. (Preliminary version: http://math.sfsu.edu/gubeladze/publications/kripo.html)

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J. Gubeladze, The nilpotence conjecture in $ K$-theory of toric varieties, Invent. Math. 160 (2005), 173-216. MR 2129712 (2006d:145057)

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W. van der Kallen, Descent for the K-theory of polynomial rings, Math. Z. 191 (1986), 405-415. MR 0824442 (87h:13012)

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H. Lindel, On the Bass-Quillen conjecture concerning projective modules over polynomial rings, Invent. Math. 65 (1981), 319-323. MR 0641133 (83g:13009)

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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)

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R. Swan, Néron-Popescu desingularization, in Algebra and Geometry, 135-192, Lect. Algebra Geom. 2, Internat. Press, Cambridge, MA, 1998. MR 1697953 (2000h:13006)

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T. Vorst, Localization of the $ K$-theory of polynomial extensions, Math. Ann. 244 (1979), 33-53. MR 0550060 (80k:18016)

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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: 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
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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