[Résolutions de Beilinson sur espaces projectifs à poids]
On étend aux espaces projectifs à poids le théorème de Beilinson [Funct. Anal. Appl. 12 (1978) 214–216], qui décrit la catégorie derivée bornée des faisceaux cohérents sur . Pour obtenir ce résultat on considère, au lieu de la catégorie habituelle des faisceaux cohérents, une certaine catégorie de faisceaux cohérents gradués (qui lui est équivalente dans le cas de ).
Beilinson's theorem [Funct. Anal. Appl. 12 (1978) 214–216], which describes the bounded derived category of coherent sheaves on , is extended to weighted projective spaces. This result is obtained by considering, instead of the usual category of coherent sheaves, a suitable category of graded coherent sheaves (which is equivalent in the case of ).
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@article{CRMATH_2003__336_1_35_0,
author = {Canonaco, Alberto},
title = {Beilinson resolutions on weighted projective spaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {35--40},
publisher = {Elsevier},
volume = {336},
number = {1},
year = {2003},
doi = {10.1016/S1631-073X(02)00004-3},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)00004-3/}
}
TY - JOUR AU - Canonaco, Alberto TI - Beilinson resolutions on weighted projective spaces JO - Comptes Rendus. Mathématique PY - 2003 SP - 35 EP - 40 VL - 336 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)00004-3/ DO - 10.1016/S1631-073X(02)00004-3 LA - en ID - CRMATH_2003__336_1_35_0 ER -
%0 Journal Article %A Canonaco, Alberto %T Beilinson resolutions on weighted projective spaces %J Comptes Rendus. Mathématique %D 2003 %P 35-40 %V 336 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)00004-3/ %R 10.1016/S1631-073X(02)00004-3 %G en %F CRMATH_2003__336_1_35_0
Canonaco, Alberto. Beilinson resolutions on weighted projective spaces. Comptes Rendus. Mathématique, Tome 336 (2003) no. 1, pp. 35-40. doi : 10.1016/S1631-073X(02)00004-3. http://archive.numdam.org/articles/10.1016/S1631-073X(02)00004-3/
[1] Tilting sheaves in representation theory of algebras, Manuscripta Math., Volume 60 (1988), pp. 323-347
[2] Coherent sheaves on and problems of linear algebra, Funct. Anal. Appl., Volume 12 (1978), pp. 214-216
[3] The derived category of coherent sheaves on , Selecta Math. Soviet., Volume 3 (1983–84), pp. 233-237
[4] A Beilinson-type theorem for coherent sheaves on weighted projective spaces, J. Algebra, Volume 225 (2000), pp. 28-46
[5] A. Canonaco, Beilinson resolutions on weighted projective spaces, Preprint, 2001
[6] Weighted projective varieties, Proc. Vancouver 1981, Lecture Notes in Math., 956, Springer, 1982, pp. 34-71
[7] Residues and Duality, Lecture Notes in Math., 20, Springer, Heidelberg, 1966
[8] Des catégories derivées des catégories abéliennes, Astérisque, Volume 239 (1996)
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