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Transactions of the American Mathematical Society

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Horrocks theory and the Bernstein-Gel'fand-Gel'fand correspondence

Authors: I. Coanda and G. Trautmann
Journal: Trans. Amer. Math. Soc. 358 (2006), 1015-1031
MSC (2000): Primary 14F05, 15A75, 16E05
Published electronically: March 31, 2005
MathSciNet review: 2187643
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Abstract: We construct an explicit equivalence between a category of complexes over the exterior algebra, which we call HT-complexes, and the stable category of vector bundles on the corresponding projective space, essentially translating into more fancy terms the results of Trautmann (1978) which, in turn, were influenced by ideas of Horrocks (1964), (1980). However, the result expressed by Theorem 5.1 and its corollary, which establishes a relation between the Tate resolutions over the exterior algebra (described in a paper by Eisenbud, Fløystad, and Schreyer) and HT-complexes, might be new, although, perhaps, not a surprise to experts.

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Additional Information

I. Coanda
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO–70700 Bucharest, Romania

G. Trautmann
Affiliation: Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schrödinger-Straße, D-67663 Kaiserslautern, Germany

Received by editor(s): December 11, 2003
Received by editor(s) in revised form: March 24, 2004
Published electronically: March 31, 2005
Additional Notes: The first author was partially supported by DFG and by CERES grant 152/2001 of the Romanian Ministry of Education and Research
The research of the second author was supported by the DFG-Schwerpunktprogramm 1094
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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