@book{AST_2012__345__R1_0,
author = {Kashiwara, Masaki and Schapira, Pierre},
title = {Deformation quantization modules},
series = {Ast\'erisque},
year = {2012},
publisher = {Soci\'et\'e math\'ematique de France},
number = {345},
mrnumber = {3012169},
zbl = {1260.32001},
language = {en},
url = {https://www.numdam.org/item/AST_2012__345__R1_0/}
}
Kashiwara, Masaki; Schapira, Pierre. Deformation quantization modules. Astérisque, no. 345 (2012), 159 p. https://www.numdam.org/item/AST_2012__345__R1_0/
[1] , (eds.) - Théorie des topos et cohomologie étale des schémas. Tome 2, Lecture Notes in Math., vol. 270, Springer, 1972, Séminaire de Géométrie Algébrique du Bois-Marie 1963-1964 (SGA 4). Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. | Zbl
[2] , , , et - "Deformation theory and quantization. I. Deformations of symplectic structures", Ann. Physics 111 (1978), p. 61-110. | MR | Zbl | DOI
[3] , et - "Non-commutative tori and Fourier-Mukai duality", Compos. Math. 143 (2007), p. 423-475. | MR | Zbl | DOI
[4] - "Quantization", Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), p. 1116-1175. | MR | Zbl
[5] , "General concept of quantization", Comm. Math. Phys. 40 (1975), p. 153-174. | MR | Zbl | DOI
[6] - "A relation between Hochschild homology and cohomology for Gorenstein rings", Proc. Amer. Math. Soc. 126 (1998), p. 1345-1348. | MR | Zbl | DOI
[7] - "On global deformation quantization in the algebraic case", J. Algebra 315 (2007), p. 326-395. | MR | Zbl | DOI
[8] et - "Fedosov quantization in algebraic context", Mosc. Math. J. 4 (2004), p. 559-592, 782. | MR | Zbl | DOI
[9] - "Complex star algebras", Math. Phys. Anal. Geom. 2 (1999), p. 113-139. | MR | Zbl | DOI
[10] - "On the classification of -gerbes and -stacks", Astérisque 225 (1994). | MR | Zbl | Numdam
[11] , , et - "Algebraic index theorem for symplectic deformations of gerbes", in Noncommutative geometry and global analysis, Contemp. Math., vol. 546, Amer. Math. Soc., 2011, p. 23-38. | MR | Zbl | DOI
[12] , , et - "Deformation quantization of gerbes", Adv. Math. 214 (2007), p. 230-266. | MR | Zbl | DOI
[13] , , et , "Chern character for twisted complexes", in Geometry and dynamics of groups and spaces, Progr. Math., vol. 265, Birkhäuser, 2008, p. 309-324. | MR | Zbl
[14] , et - "Riemann-Roch theorems via deformation quantization. I, II", Adv. Math. 167 (2002), p. 1-25, 26-73. | MR | Zbl | DOI
[15] et - "The homology of algebras of pseudodifferential symbols and the noncommutative residue", -Theory 1 (1987), p. 385-403. | MR | Zbl | DOI
[16] et - "Weak quantization of Poisson structures", J. Geom. Phys. 61 (2011), p. 1401-1414. | MR | Zbl | DOI
[17] - "The Mukai pairing. II. The Hochschild-Kostant-Rosenberg isomorphism", Adv. Math. 194 (2005), p. 34-66. | MR | Zbl | DOI
[18] et - "The Mukai pairing. I. A categorical approach", New York J. Math. 16 (2010), p. 61-98. | MR | Zbl | EuDML
[19] - "GAGA for -algebroids", Rend. Semin. Mat. Univ. Padova 123 (2010), p. 211-231. | MR | Zbl | EuDML | Numdam | DOI
[20] , et - "Regular holonomic -modules", Publ. Res. Inst. Math. Sci. 47 (2011), p. 221-255. | MR | Zbl
[21] et - "Deformation quantization of complex involutive submanifolds", in Noncommutative geometry and physics, World Sci. Publ., Hackensack, NJ, 2005, p. 127-137. | MR
[22] et - "Quantization of complex Lagrangian submanifolds", Adv. Math. 213 (2007), p. 358-379. | MR | Zbl | DOI
[23] - "The Van den Bergh duality and the modular symmetry of a Poisson variety", Selecta Math. (N.S.) 14 (2009), p. 199-228. | MR | Zbl | DOI
[24] et - "An algebraic index theorem for Poisson manifolds", J. reine angew. Math. 633 (2009), p. 77-113. | MR | Zbl
[25] - Deformation quantization and index theory, Mathematical Topics, vol. 9, Akademie Verlag, 1996. | MR | Zbl
[26] , et - "Riemann-Roch-Hirzebruch theorem and topological quantum mechanics", preprint arXiv:math.QA/0401400.
[27] et - "Riemann-Roch theorem and Lie algebra cohomology. I", in Proceedings of the Winter School on Geometry and Physics (Srní, 1988), vol. 21, 1989, p. 15-52. | MR | Zbl | EuDML
[28] - "The integrability of the characteristic variety", Amer. J. Math. 103 (1981), p. 445-468. | MR | Zbl | DOI
[29] - Cohomologie non abélienne, Die Grund. Math. Wiss., vol. 179, Springer, 1971. | MR | Zbl
[30] - Topologie algébrique et théorie des faisceaux, Actualités Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13, Hermann, 1958. | MR | Zbl
[31] - "Ein Theorem der analytischen Garbentheorie und die Modulräume complexer Strukturen", Publ. IHÉS 5 (1960). | MR | EuDML | Numdam
[32] - "On a conjecture of Kashiwara relating Chern and Euler classes of -modules-modules", preprint arXiv:0910.5384. | MR | Zbl
[33] - "Éléments de Géométrie Algébrique III, Étude cohomologique des faisceaux cohérents I", Publ. IHÉS 11 (1961). | MR | Numdam
[34] - "Espaces analytiques relatifs et théorème de finitude", Math. Ann. 205 (1973), p. 13-54. | MR | Zbl | EuDML | DOI
[35] - Fourier-Mukai transforms in algebraic geometry, Oxford Mathematical Monographs, The Clarendon Press Oxford Univ. Press, 2006. | Zbl | MR
[36] - "On the maximally overdetermined system of linear differential equations. I", Publ. Res. Inst. Math. Sci. 10 (1974/75), p. 563-579. | MR | Zbl | DOI
[37] , "Quantization of contact manifolds", Publ. Res. Inst. Math. Sci. 32 (1996), p. 1-7. | MR | Zbl | DOI
[38] , -modules and microlocal calculus, Translations of Mathematical Monographs, vol. 217, Amer. Math. Soc., 2003. | MR | Zbl
[39] , Letter to Pierre Schapira, 18/11/1991.
[40] et - "Systems of differential equations with regular singularities and their boundary value problems", Ann. Math. 106 (1977), p. 145-200. | MR | Zbl | DOI
[41] et - Sheaves on manifolds, Grund. Math. Wiss., vol. 292, Springer, 1990. | MR | Zbl
[42] et , "Moderate and formal cohomology associated with constructible sheaves", Mém. Soc. Math. France (N.S.) 64 (1996). | MR | Zbl | EuDML | Numdam
[43] et , Categories and sheaves, Grund. Math. Wiss., vol. 332, Springer, 2006. | MR | Zbl
[44] et , "Constructibility and duality for simple holonomic modules on complex symplectic manifolds", Amer. J. Math. 130 (2008), p. 207-237. | MR | Zbl | DOI
[45] et , "Modules over deformation quantization algebroids : an overview", Lett. Math. Phys. 88 (2009), p. 79-99. | MR | Zbl | DOI
[46] et ,"Deformation quantization modules", preprint arXiv: 1003.3304. | MR | Zbl | Numdam
[47] - "Deformation quantization of algebraic varieties", Lett. Math. Phys. 56 (2001), p. 271-294. | MR | Zbl | DOI
[48] , "Deformation quantization of Poisson manifolds", Lett. Math. Phys. 66 (2003), p. 157-216. | MR | Zbl | DOI
[49] - "Sur la catégorie dérivée des -modules filtrés", in Algebraic geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., vol. 1016, Springer, 1983, p. 151-237. | MR | Zbl | DOI
[50] - "The Atiyah class, Hochschild cohomology and the Riemann-Roch theorem", J. Lond. Math. Soc. 79 (2009), p. 129-143. | MR | Zbl | DOI
[51] - "The additivity of traces in triangulated categories", Adv. Math. 163 (2001), p. 34-73. | MR | Zbl | DOI
[52] - "Classification of deformation quantization algebroids on complex symplectic manifolds", Publ. Res. Inst. Math. Sci. 44 (2008), p. 725-748. | MR | Zbl | DOI
[53] et - "Stacks of quantization-deformation modules on complex symplectic manifolds", Int. Math. Res. Not. 2004 (2004), p. 2637-2664. | MR | Zbl | DOI
[54] - "On a question of Quillen", Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 45(93) (2002), p. 209-212. | MR | Zbl
[55] - "The relative Riemann-Roch theorem from Hochschild homology", New York J. Math. 14 (2008), p. 643-717. | MR | Zbl | EuDML
[56] , et - "Microfunctions and pseudo-differential equations", in Hyperfunctions and pseudo-differential equations (Proc. Conf., Katata, 1971 ; dedicated to the memory of André Martineau), Springer, 1973, p. 265-529. Lecture Notes in Math., Vol. 287. | MR | Zbl
[57] - Microdifferential systems in the complex domain, Grund. Math. Wiss., vol. 269, Springer, 1985. | MR | Zbl
[58] et - "Elliptic pairs. II. Euler class and relative index theorem", Astérisque 224 (1994), p. 61-98. | MR | Zbl | Numdam
[59] - "Hirzebruch-Riemann-Roch theorem for DG algebras", preprint arXiv:math/0710.1937. | Zbl
[60] - "Néron-Popescu desingularization", in Algebra and geometry (Taipei, 1995), Lect. Algebra Geom., vol. 2, Int. Press, Cambridge, MA, 1998, p. 135-192. | MR | Zbl
[61] - "Cyclic homology of pseudodifferential operators and noncommutative Euler class", C. R. Acad. Sci. Paris Ser. I Math. 306 (1988), p. 321-325. | MR | Zbl
[62] - "The continuous Hochschild cochain complex of a scheme", Canad. J. Math. 54 (2002), p. 1319-1337. | MR | Zbl | DOI
[63] , "Deformation quantization in algebraic geometry", Adv. Math. 198 (2005), p. 383-432 | MR | Zbl | DOI
, "Deformation quantization in algebraic geometry", erratum : Adv. Math. 217 (2008), 2897-2906. | MR | Zbl
[64] , "Twisted deformation quantization of algebraic varieties", preprint arXiv:math.AG/0905.0488. | MR | Zbl | DOI






