Geodesic
Descent theory for semiorthogonal decompositions
Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 645-676

Voir la notice de l'article provenant de la source Math-Net.Ru

We put forward a method for constructing semiorthogonal decompositions of the derived category of $G$-equivariant sheaves on a variety $X$ under the assumption that the derived category of sheaves on $X$ admits a semiorthogonal decomposition with components preserved by the action of the group $G$ on $X$. This method is used to obtain semiorthogonal decompositions of equivariant derived categories for projective bundles and blow-ups with a smooth centre as well as for varieties with a full exceptional collection preserved by the group action. Our main technical tool is descent theory for derived categories. Bibliography: 12 titles.
Keywords: derived category, descent theory, algebraic variety.
Mots-clés : semiorthogonal decomposition 
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     title = {Descent theory for semiorthogonal decompositions},
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A. Elagin. Descent theory for semiorthogonal decompositions. Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 645-676. http://geodesic.mathdoc.fr/item/SM_2012_203_5_a1/