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McKay correspondence and derived equivalences

Abstract : The first chapter shows by toric methods ($G-$graphs) that for any positive integer $n$, the quotient of the affine $n-$dimensional space by the cyclic group $G_n$ of order $2^n-1$ has the $G_n-$Hilbert scheme as smooth crepant resolution. The second chapter contains results on algebraic stacks (construction of a smooth algebraic stack associated to a log-pair). The third chapter shows the equivalence of the bounded derived category of $G_n-$equivariant coherent sheaves on the affine space with that of coherent sheaves on the resolution $G_n-$Hilb. Chpater 4 gives a geometric equivalent of Broué's conjecture via the McKay correspondence. The Annexe contains results on trihedral groups, including a magma programme.
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Contributor : Magda Sebestean <>
Submitted on : Thursday, March 30, 2006 - 4:35:35 PM
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  • HAL Id : tel-00012064, version 1

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Magda Sebestean. McKay correspondence and derived equivalences. Mathematics [math]. Université Paris-Diderot - Paris VII, 2005. English. ⟨tel-00012064⟩

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