## Horrocks theory and the Bernstein-Gel’fand-Gel’fand correspondence

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- by I. Coandă and G. Trautmann PDF
- Trans. Amer. Math. Soc.
**358**(2006), 1015-1031 Request permission

## 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.## References

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## Additional Information

**I. Coandă**- Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO–70700 Bucharest, Romania
- MR Author ID: 50030
- Email: Iustin.Coanda@imar.ro
**G. Trautmann**- Affiliation: Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schrödinger-Straße, D-67663 Kaiserslautern, Germany
- Email: trm@mathematik.uni-kl.de
- 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 - © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**358**(2006), 1015-1031 - MSC (2000): Primary 14F05, 15A75, 16E05
- DOI: https://doi.org/10.1090/S0002-9947-05-03755-4
- MathSciNet review: 2187643