?. K. Then, is fully faithful if, and only if, ? K| X i ×Y i : D b (Y i ) ? D b (X i ) is fully faithful for i = 1, 2. Idea of a proof

X. Supp? and K. , O y ? ) ? X i . For an integer k we have

?. K. Now, O y )| X i is isomorphic to ? K| X i ×Y i (O y ) We conclude that

R. Bezrukavnikov and D. Kaledin, McKay equivalence for symplectic resolutions of singularities, E-print math, p.401002

T. Bridgeland, Equivalences of Triangulated Categories and Fourier-Mukai Transforms, Bulletin of the London Mathematical Society, vol.31, issue.1, pp.25-34, 1999.
DOI : 10.1112/S0024609398004998

T. Bridgeland, A. King, and M. Reid, The McKay correspondence as an equivalence of derived categories, Journal of the American Mathematical Society, vol.14, issue.03, pp.535-554, 2001.
DOI : 10.1090/S0894-0347-01-00368-X

L. Chiang and S. S. , Orbifolds and finite group representations, International Journal of Mathematics and Mathematical Sciences, vol.26, issue.11, pp.649-669, 2001.
DOI : 10.1155/S0161171201020154

URL : http://doi.org/10.1155/s0161171201020154

A. Craw, M. Reid, C. Haase, and G. Ziegler, How to calculate A-Hilb C 3 E-print math All toric local complete intersection singularities admit projective crepant resolutions, Séminaires et Congrès Tohoku Math. J, vol.6, issue.2 1, pp.129-154, 2001.

D. Dais, M. Henk, and G. Ziegler, All Abelian Quotient C.I.-Singularities Admit Projective Crepant Resolutions in All Dimensions, Advances in Mathematics, vol.139, issue.2, pp.194-239, 1998.
DOI : 10.1006/aima.1998.1751

P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Publications math??matiques de l'IH??S, vol.44, issue.1, pp.75-109, 1969.
DOI : 10.1007/BF02684599

G. Gonzalez-sprinberg and J. Verdier, Construction géométrique de la correspondance de, McKay Ann. Sci. ´ Ecole Norm. Sup, vol.4, issue.16 3, pp.409-449, 1983.

W. Fulton, Introduction to toric varieties, 1993.

A. Grothendieck, Techniques de construction et Théorie d'existance en géométrie Algébrique IV: Les schémas de Hilbert, Sém Bourbaki, vol.221, p.61, 1960.

A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique. III. Préschemas quotients, Séminaire Bourbaki, vol.6, issue.212, pp.99-118, 1995.

R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, vol.52, issue.52, 1977.
DOI : 10.1007/978-1-4757-3849-0

Y. Ito and H. Nakajima, McKay correspondence and Hilbert schemes in dimension three, Topology, vol.39, issue.6, pp.1155-1191, 2000.
DOI : 10.1016/S0040-9383(99)00003-8

Y. Ito and I. Nakamura, McKay correspondence and Hilbert schemes, Proc. Japan Acad. 72A, pp.135-138, 1996.
DOI : 10.3792/pjaa.72.135

M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1994.

Y. Kawamata, Log Crepant Birational Maps and Derived Categories E-print math, J. Math. Sci. Univ. Tokyo, vol.12, issue.2, pp.211-231, 2003.

Y. Kawamata and . Gruyter, Francia's flip and derived categories Algebraic Geometry: A volume in Memory of Paolo Francia, pp.197-215, 2001.

B. Keller, Deriving DG categories, Annales scientifiques de l'??cole normale sup??rieure, vol.27, issue.1, pp.27-63, 1994.
DOI : 10.24033/asens.1689

D. Knutson, Algebraic spaces, Lecture Notes in Mathematics, vol.203, 1971.

R. Leng, Chapters 2 and 3

D. Markouchevitch, Resolution of C 3, Math. Ann, vol.168, issue.308, pp.279-289, 1997.

J. Mckay, Graphs, singularities, and finite groups The Santa Cruz Conference on Finite Groups, Proc. Sympos. Pure Math, pp.183-186, 1979.

D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory, 1994.

I. Nakamura, Hilbert schemes of abelian group orbits, J. Algebraic Geom, vol.10, issue.4, pp.757-779, 2001.

T. Oda, Convex bodies and algebraic geometry, 1988.
DOI : 10.1007/978-3-642-72547-0

M. Reid, Young Person's Guide to Canonical Singularities, Algebraic geometry, Proc. Sympos. Pure Math, pp.345-414, 1985.

M. Reid, Journées de Géometrie Algébrique d'Angers, pp.273-310, 1979.

P. Schapira, Categories and Homological Algebra

S. Térouanne and C. De-mckay, Institut Fourier, Thèse de doctorat, 2004.

A. Vistoli, Intersection theory on algebraic stacks and on their moduli spaces, Inventiones Mathematicae, vol.58, issue.3, pp.613-670, 1989.
DOI : 10.1007/BF01388892

A. Vistoli, Introduction to algebraic stacks, lectures on " School and Conference on Intersection Theory and Moduli, pp.9-27, 2002.

A. Vistoli, Notes on Grothendieck topologies, fibered categories and descent theory