Geodesic
Semiorthogonal decompositions of derived categories of equivariant coherent sheaves
Izvestiya. Mathematics , Tome 73 (2009) no. 5, pp. 893-920

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Let $X$ be an algebraic variety with an action of an algebraic group $G$. Suppose that $X$ has a full exceptional collection of sheaves and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of the bounded derived category of $G$-equivariant coherent sheaves on $X$ into components that are equivalent to the derived categories of twisted representations of $G$. If the group is finite or reductive over an algebraically closed field of characteristic 0, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmannians and del Pezzo surfaces.
Keywords: exceptional collection, twisted sheaf.
Mots-clés : semiorthogonal decomposition 
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     author = {A. Elagin},
     title = {Semiorthogonal decompositions of derived categories of equivariant coherent sheaves},
     journal = {Izvestiya. Mathematics },
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     volume = {73},
     number = {5},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_5_a1/}
}
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A. Elagin. Semiorthogonal decompositions of derived categories of equivariant coherent sheaves. Izvestiya. Mathematics , Tome 73 (2009) no. 5, pp. 893-920. http://geodesic.mathdoc.fr/item/IM2_2009_73_5_a1/