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Nakai's conjecture for varieties smoothed by normalization
Author(s):
William
N.
Traves
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2245-2248.
MSC (1991):
Primary 13N10;
Secondary 16S32
Posted:
April 9, 1999
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Abstract:
The notion of D-simplicity is used to give a short proof that varieties whose normalization is smooth satisfy Ishibashi's extension of Nakai's conjecture to arbitrary characteristic. This gives a new proof of Nakai's conjecture for curves and Stanley-Reisner rings.
References:
- 1.
- Dieudonné, J. and Grothendieck, A. Élements de géométrie algèbrique IV. Publ. Math. I.H.E.S. 32 (1967). MR 39:220
- 2.
- Ishibashi, Yasunori. An Analogue of Nakai's Conjecture. Communications in Algebra 13 (1985), no. 3, 575-584. MR 86e:13005
- 3.
- McConnell J. C., and Robson, J. C. Noncommutative Noetherian Rings. Wiley, New York, 1987. MR 89j:16023
- 4.
- Mount, Ken R. and O. E. Villamayor. On a Conjecture of Y. Nakai. Osaka J. Math. 10 (1973), 325-327. MR 48:6073
- 5.
- Schreiner, A. On a Conjecture of Nakai. Arch. Math. 62 (1994), 506-512. MR 95f:13033
- 6.
- Seidenberg, A. Derivations and Integral Closure. Pacific J. Math. 16 (1966), no. 1, 167-173. MR 32:5686
- 7.
- Smith, K. E. The D-module Structure of F-split Rings. Mathematical Research Letters. 2 (1995), 377-386. MR 96j:13024
- 8.
- Traves, William N. Differential Operators on Monomial Rings. Journal of Pure and Applied Algebra. To appear.
- 9.
- Traves, William N. Differential Operators and Nakai's Conjecture. Ph.D. Thesis. University of Toronto (1998).
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Additional Information:
William
N.
Traves
Affiliation:
Department of Mathematics, University of Toronto, 100 St. George Street, 4th Floor, Toronto, Ontario, Canada M5S 3G3
Email:
traves@math.toronto.edu
DOI:
10.1090/S0002-9939-99-04820-0
PII:
S 0002-9939(99)04820-0
Keywords:
Differential operators,
Nakai's conjecture,
D-simple
Received by editor(s):
August 11, 1997
Received by editor(s) in revised form:
November 10, 1997
Posted:
April 9, 1999
Additional Notes:
I would like to thank Karen E. Smith for many helpful discussions. This research has been partially funded by NSERC, the NSF, the Massachusetts Intstitute of Technology and the University of Toronto.
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
1999,
American Mathematical Society
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