A note on the Nakai conjecture
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- by Paulo Brumatti, Yves Lequain, Daniel Levcovitz and Aron Simis PDF
- Proc. Amer. Math. Soc. 130 (2002), 15-21 Request permission
Abstract:
The conjectures of Zariski–Lipman and of Nakai are still open in general in the class of rings essentially of finite type over a field of characteristic zero. However, they have long been known to be true in dimension one. Here we give counterexamples to both conjectures in the class of one-dimensional pseudo-geometric local domains that contain a field of characteristic zero. Likewise, in connection with a recent result of Traves on the Nakai conjecture, we also show that their hypothesis of finite generation of the integral closure cannot be removed even in the class of local domains containing a field of characteristic zero.References
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Additional Information
- Paulo Brumatti
- Affiliation: IMECC–UNICAMP, 13081-970 Campinas, São Paulo, Brazil
- Email: brumatti@ime.unicamp.br
- Yves Lequain
- Affiliation: Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, J. Botânico, 22460-320, Rio de Janeiro, RJ, Brazil
- Email: ylequain@impa.br
- Daniel Levcovitz
- Affiliation: Instituto de Ciências Matemáticas e de Computação, USP-SC, Av. Dr. Carlos Botelho, 1465, 13560-970 São Carlos, SP, Brazil
- Email: lev@icmsc.sc.usp.br
- Aron Simis
- Affiliation: Departamento de Matemática, CCEN, Universidade Federal de Pernambuco, 50740-540 Recife, PE, Brazil
- MR Author ID: 162400
- Email: aron@dmat.ufpe.br
- Received by editor(s): January 11, 2000
- Received by editor(s) in revised form: May 19, 2000
- Published electronically: April 26, 2001
- Additional Notes: The authors were partially supported by CNPq and by a grant from the group ALGA-PRONEX/MCT
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 15-21
- MSC (2000): Primary 13M05, 13M10, 13N15, 13B22; Secondary 14F10, 12H05, 13B25, 13F25
- DOI: https://doi.org/10.1090/S0002-9939-01-05983-4
- MathSciNet review: 1855614