Geodesic
The Horrocks correspondence for coherent sheaves on projective spaces
Homology, homotopy, and applications, Tome 12 (2010) no. 1, pp. 327-353.

Voir la notice de l'article provenant de la source International Press of Boston

We establish an equivalence between the stable category of coherent sheaves (satisfying a mild restriction) on a projective space and the homotopy category of a certain class of minimal complexes of free modules over the exterior algebra Koszul dual to the homogeneous coordinate algebra of the projective space. We also relate these complexes to the Tate resolutions of the respective sheaves. In this way, we extend from vector bundles to coherent sheaves the results of G. Trautmann and the author (2005), which interpret in terms of the BGG correspondence the results of Trautmann (1978) about the correspondence of Horrocks (1964), (1977). We also give direct proofs of the BGG correspondences for graded modules and for coherent sheaves and of the theorem of Eisenbud, Fløystad and Schreyer (2003) describing the linear part of the Tate resolution associated to a coherent sheaf. Moreover, we provide an explicit description of the quotient of the Tate resolution by its linear strand corresponding to the module of global sections of the various twists of the sheaf.
DOI : 10.4310/HHA.2010.v12.n1.a16
Classification : 13A02, 14F05, 18E30
Keywords: coherent sheaf, projective space, stable category, derived category 
@article{HHA_2010_12_1_a16,
     author = {Iustin Coand\u{a}},
     title = {The {Horrocks} correspondence for coherent sheaves on projective spaces},
     journal = {Homology, homotopy, and applications},
     pages = {327--353},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2010},
     doi = {10.4310/HHA.2010.v12.n1.a16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2010.v12.n1.a16/}
}
TY  - JOUR
AU  - Iustin Coandă
TI  - The Horrocks correspondence for coherent sheaves on projective spaces
JO  - Homology, homotopy, and applications
PY  - 2010
SP  - 327
EP  - 353
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2010.v12.n1.a16/
DO  - 10.4310/HHA.2010.v12.n1.a16
LA  - en
ID  - HHA_2010_12_1_a16
ER  - 
%0 Journal Article
%A Iustin Coandă
%T The Horrocks correspondence for coherent sheaves on projective spaces
%J Homology, homotopy, and applications
%D 2010
%P 327-353
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2010.v12.n1.a16/
%R 10.4310/HHA.2010.v12.n1.a16
%G en
%F HHA_2010_12_1_a16
Iustin Coandă. The Horrocks correspondence for coherent sheaves on projective spaces. Homology, homotopy, and applications, Tome 12 (2010) no. 1, pp. 327-353. doi : 10.4310/HHA.2010.v12.n1.a16. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2010.v12.n1.a16/

Cité par Sources :