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$ K$-regularity, $ cdh$-fibrant Hochschild homology, and a conjecture of Vorst

Authors: G. Cortiñas, C. Haesemeyer and C. Weibel
Journal: J. Amer. Math. Soc. 21 (2008), 547-561
MSC (2000): Primary 19D35; Secondary 14F20, 13D03, 19D55
Published electronically: May 16, 2007
MathSciNet review: 2373359
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Abstract: In this paper we prove that for an affine scheme essentially of finite type over a field $ F$ and of dimension $ d$, $ K_{d+1}$-regularity implies regularity, assuming that the characteristic of $ F$ is zero. This verifies a conjecture of Vorst.

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Additional Information

G. Cortiñas
Affiliation: Departamento Matemática, FCEyN-Universidad de Buenos Aires, Ciudad Universitaria Pab 1, 1428 Buenos Aires, Argentina, and Departamento Álgebra, Faculdad de Ciencias, Prado de la Magdalena s/n, 47005 Valladolid, Spain

C. Haesemeyer
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Address at time of publication: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 SEO, 851 South Morgan Street, Chicago, Illinois 60607-7045

C. Weibel
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08901

Received by editor(s): May 15, 2006
Published electronically: May 16, 2007
Additional Notes: The first author’s research was partially supported by FSE and by grants ANPCyT PICT 03-12330, UBACyT-X294, JCyL VA091A05, and MEC MTM00958.
The last author’s research was partially supported by NSA grant MSPF-04G-184.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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