McKay Equivalence for Symplectic Resolutions of Quotient Singularities
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 20-42.

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

An arbitrary crepant resolution $X$ of the quotient $V/G$ of a symplectic vector space $V$ by the action of a finite subgroup $G\subset\mathrm{Sp}(V)$ is considered. It is proved that the derived category of coherent sheaves on $X$ is equivalent to the derived category of $G$-equivariant coherent sheaves on $V$.
@article{TM_2004_246_a2,
     author = {R. V. Bezrukavnikov and D. B. Kaledin},
     title = {McKay {Equivalence} for {Symplectic} {Resolutions} of {Quotient} {Singularities}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {20--42},
     publisher = {mathdoc},
     volume = {246},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_246_a2/}
}
TY  - JOUR
AU  - R. V. Bezrukavnikov
AU  - D. B. Kaledin
TI  - McKay Equivalence for Symplectic Resolutions of Quotient Singularities
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2004
SP  - 20
EP  - 42
VL  - 246
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2004_246_a2/
LA  - ru
ID  - TM_2004_246_a2
ER  - 
%0 Journal Article
%A R. V. Bezrukavnikov
%A D. B. Kaledin
%T McKay Equivalence for Symplectic Resolutions of Quotient Singularities
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2004
%P 20-42
%V 246
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2004_246_a2/
%G ru
%F TM_2004_246_a2
R. V. Bezrukavnikov; D. B. Kaledin. McKay Equivalence for Symplectic Resolutions of Quotient Singularities. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 20-42. http://geodesic.mathdoc.fr/item/TM_2004_246_a2/

[1] Berthelot P., Ogus A., Notes on crystalline cohomology, Princeton Univ. Press, Univ. Tokyo Press, Princeton, NJ, Tokyo, 1978 | MR | Zbl

[2] Bezrukavnikov R., Mirković I., Rumynin D., Localization of modules for a semisimple Lie algebra in prime characteristic, , 2002 arXiv: /math.RT/0205144 | MR

[3] Bridgeland T., King A., Reid M., “The McKay correspondence as an equivalence of derived categories”, J. Amer. Math. Soc., 14 (2001), 535–554 | DOI | MR | Zbl

[4] Bondal A. I., Kapranov M. M., “Predstavimye funktory, funktory Serra i perestroiki”, Izv. AN SSSR. Ser. mat., 53 (1989), 1183–1205 | MR

[5] Bondal A., Orlov D., “Derived categories of coherent sheaves”, Proc. Intern. Congr. Math. (Beijing, 2002), 2, Higher Ed. Press, Beijing, 2002, 47–56 | MR

[6] Gabber O., “Some theorems on Azumaya algebras”, Groupe de Brauer, Semin. Les Plans-sur-Bex (1980. Berlin), Lect. Notes Math., 844, Springer, New York, 1981, 129–209 | MR

[7] Gonzalez-Sprinberg G., Verdier J.-L., “Construction géométrique de la correspondance de McKay”, Ann. Sci. École Norm. Supér, 16 (1983), 409–449 | MR | Zbl

[8] Haiman M., “Hilbert schemes, polygraphs, and the Macdonald positivity conjecture”, J. Amer. Math. Soc., 14 (2001), 941–1006 | DOI | MR | Zbl

[9] Hartshorne R., Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne, Lect. Notes Math., 20, Springer, 1966, Berlin, New York | MR | Zbl

[10] Ito Y., Nakamura I., “McKay correspondence and Hilbert schemes”, Proc. Japan Acad. A: Math. Sci., 72:7 (1996), 135–138 | DOI | MR | Zbl

[11] Kaledin D., Dynkin diagrams and crepant resolutions of singularities, , 1999 arXiv: /math.AG/9903157

[12] Kaledin D., Sommese vanishing for non-compact manifolds, , 2003 arXiv: /math.AG/0312271

[13] Kapranov M., “Noncommutative geometry based on commutator expansions”, J. Reine und Angew. Math., 505 (1998), 73–118 | MR | Zbl

[14] Kapranov M., Vasserot E., “Kleinian singularities, derived categories and Hall algebras”, Math. Ann., 316 (2000), 565–576 | DOI | MR | Zbl

[15] Keller B., “On the cyclic homology of exact categories”, J. Pure and Appl. Algebra, 136 (1999), 1–56 | DOI | MR | Zbl

[16] King A., “Moduli of representations of finite-dimensional algebras”, Quart. J. Math. Oxford. Ser. 2, 45 (1994), 515–530 | DOI | MR | Zbl

[17] Kronheimer P. B., “The construction of ALE spaces as hyper-Kähler quotients”, J. Diff. Geom., 29 (1989), 665–683 | MR | Zbl

[18] Lusztig G., “On quiver varieties”, Adv. Math., 136 (1998), 141–182 | DOI | MR | Zbl

[19] Milne J.S., Étale cohomology, Princeton Math. Ser., 33, Princeton Univ. Press, Princeton, 1980 ; Милн Дж., Этальные когомологии, Мир, М., 1982 | MR | Zbl | MR

[20] Nakajima H., “Quiver varieties and Kac–Moody algebras”, Duke Math. J., 91 (1998), 515–560 | DOI | MR | Zbl

[21] Nakajima H., Lectures on Hilbert schemes of points on surfaces, Univ. Lect. Ser., 18, Amer. Math. Soc., Providence, RI, 1999 | MR | Zbl

[22] Reid M., McKay correspondence, , 1997 arXiv: /alg-geom/9702016 | MR