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Categorical cell decomposition of quantized symplectic algebraic varieties

Gwyn Bellamy, Christopher Dodd, Kevin McGerty and Thomas Nevins

Geometry & Topology 21 (2017) 2601–2681
Bibliography
1 K Ardakov, S Wadsley, On irreducible representations of compact p–adic analytic groups, Ann. of Math. 178 (2013) 453 MR3071505
2 M Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969) 23 MR0268188
3 A Beĭlinson, J Bernstein, A proof of Jantzen conjectures, from: "I M Gel’fand seminar" (editor S Gindikin), Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 1 MR1237825
4 G Bellamy, C Dodd, K McGerty, T Nevins, Lagrangian skeleta and Koszul duality on bionic symplectic varieties, in preparation
5 G Bellamy, T Kuwabara, On deformation quantizations of hypertoric varieties, Pacific J. Math. 260 (2012) 89 MR3001787
6 P Berthelot, 𝒟–modules arithmétiques, I : Opérateurs différentiels de niveau fini, Ann. Sci. École Norm. Sup. 29 (1996) 185 MR1373933
7 R Bezrukavnikov, D Kaledin, Fedosov quantization in algebraic context, Mosc. Math. J. 4 (2004) 559 MR2119140
8 R V Bezrukavnikov, D B Kaledin, McKay equivalence for symplectic resolutions of quotient singularities, Tr. Mat. Inst. Steklova 246 (2004) 20 MR2101282
9 R Bezrukavnikov, I Losev, Etingof conjecture for quantized quiver varieties, preprint (2013) arXiv:1309.1716
10 A Białynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. 98 (1973) 480 MR0366940
11 A Białynicki-Birula, Some properties of the decompositions of algebraic varieties determined by actions of a torus, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976) 667 MR0453766
12 T Braden, A Licata, N Proudfoot, B Webster, Quantizations of conical symplectic resolutions, II : Category 𝒪 and symplectic duality, preprint (2014) arXiv:1407.0964
13 T Braden, N Proudfoot, B Webster, Quantizations of conical symplectic resolutions, I: Local and global structure, preprint (2012) arXiv:1208.3863
14 N Chriss, V Ginzburg, Representation theory and complex geometry, Birkhäuser (1997) MR1433132
15 A D’Agnolo, M Kashiwara, On quantization of complex symplectic manifolds, Comm. Math. Phys. 308 (2011) 81 MR2842971
16 A D’Agnolo, P Polesello, Deformation quantization of complex involutive submanifolds, from: "Noncommutative geometry and physics" (editors Y Maeda, N Tose, N Miyazaki, S Watamura, D Sternheimer), World Sci. (2005) 127 MR2186385
17 A D’Agnolo, P Schapira, Quantization of complex Lagrangian submanifolds, Adv. Math. 213 (2007) 358 MR2331247
18 C Dodd, K Kremnizer, A localization theorem for finite W–algebras, preprint (2009) arXiv:0911.2210
19 V Dolgushev, The Van den Bergh duality and the modular symmetry of a Poisson variety, Selecta Math. 14 (2009) 199 MR2480714
20 J P Dufour, N T Zung, Poisson structures and their normal forms, 242, Birkhäuser (2005) MR2178041
21 D Eisenbud, Commutative algebra: with a view toward algebraic geometry, 150, Springer (1995) MR1322960
22 P Etingof, V Ginzburg, Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147 (2002) 243 MR1881922
23 L Fresse, Borel subgroups adapted to nilpotent elements of standard Levi type, Represent. Theory 18 (2014) 341 MR3272063
24 V Ginsburg, Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986) 327 MR833194
25 V Ginzburg, Harish-Chandra bimodules for quantized Slodowy slices, Represent. Theory 13 (2009) 236 MR2515934
26 I G Gordon, I Losev, On category 𝒪 for cyclotomic rational Cherednik algebras, J. Eur. Math. Soc. 16 (2014) 1017 MR3210960
27 I G Gordon, J T Stafford, The Auslander–Gorenstein property for –algebras, J. Algebra 399 (2014) 102 MR3144580
28 A Grothendieck, Eléments de géométrie algébrique, III : Étude cohomologique des faisceaux cohérents, I, Inst. Hautes Études Sci. Publ. Math. 11 (1961) 5 MR0163910
29 V Guillemin, S Sternberg, Symplectic techniques in physics, Cambridge University Press (1990) MR1066693
30 R Hartshorne, On the De Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. 45 (1975) 5 MR0432647
31 R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
32 R Hotta, K Takeuchi, T Tanisaki, D–modules, perverse sheaves, and representation theory, 236, Birkhäuser (2008) MR2357361
33 D Huybrechts, E Macrì, P Stellari, Formal deformations and their categorical general fibre, Comment. Math. Helv. 86 (2011) 41 MR2745275
34 L Illusie, Complexe cotangent et déformations, I, 239, Springer (1971) MR0491680
35 D Kaledin, Derived equivalences by quantization, Geom. Funct. Anal. 17 (2008) 1968 MR2399089
36 J Kamnitzer, P Tingley, B Webster, A Weekes, O Yacobi, Highest weights for truncated shifted Yangians and product monomial crystals, preprint (2015) arXiv:1511.09131
37 J Kamnitzer, B Webster, A Weekes, O Yacobi, Yangians and quantizations of slices in the affine Grassmannian, Algebra Number Theory 8 (2014) 857 MR3248988
38 M M Kapranov, On DG-modules over the de Rham complex and the vanishing cycles functor, from: "Algebraic geometry" (editors S Bloch, I Dolgachev, W Fulton), Lecture Notes in Math. 1479, Springer (1991) 57 MR1181207
39 M Kashiwara, Quantization of contact manifolds, Publ. Res. Inst. Math. Sci. 32 (1996) 1 MR1384750
40 M Kashiwara, R Rouquier, Microlocalization of rational Cherednik algebras, Duke Math. J. 144 (2008) 525 MR2444305
41 M Kashiwara, P Schapira, Categories and sheaves, 332, Springer (2006) MR2182076
42 M Kashiwara, P Schapira, Deformation quantization modules, 345, Soc. Math. France (2012) MR3012169
43 B Keller, On the cyclic homology of ringed spaces and schemes, Doc. Math. 3 (1998) 231 MR1647519
44 B Keller, On the cyclic homology of exact categories, J. Pure Appl. Algebra 136 (1999) 1 MR1667558
45 F Knop, Weyl groups of Hamiltonian manifolds, I, preprint (1997) arXiv:dg-ga/9712010
46 R Kodera, K Naoi, Loewy series of Weyl modules and the Poincaré polynomials of quiver varieties, Publ. Res. Inst. Math. Sci. 48 (2012) 477 MR2973389
47 I Losev, Quantized symplectic actions and W–algebras, J. Amer. Math. Soc. 23 (2010) 35 MR2552248
48 I Losev, Finite-dimensional representations of W–algebras, Duke Math. J. 159 (2011) 99 MR2817650
49 I Losev, Isomorphisms of quantizations via quantization of resolutions, Adv. Math. 231 (2012) 1216 MR2964603
50 I Losev, Etingof conjecture for quantized quiver varieties, II: Affine quivers, preprint (2014) arXiv:1405.4998
51 I Losev, On categories O for quantized symplectic resolutions, preprint (2015) arXiv:1502.00595
52 J C McConnell, J C Robson, Noncommutative Noetherian rings, 30, Amer. Math. Soc. (2001) MR1811901
53 K McGerty, T Nevins, Derived equivalence for quantum symplectic resolutions, Selecta Math. 20 (2014) 675 MR3177930
54 K McGerty, T Nevins, Kirwan surjectivity for quiver varieties, preprint (2016) arXiv:1610.08121
55 D Nadler, Fukaya categories as categorical Morse homology, Symmetry Integrability Geom. Methods Appl. 10 (2014) MR3210617
56 H Nakajima, Lectures on Hilbert schemes of points on surfaces, 18, Amer. Math. Soc. (1999) MR1711344
57 H Nakajima, K Yoshioka, Instanton counting on blowup, I : 4–dimensional pure gauge theory, Invent. Math. 162 (2005) 313 MR2199008
58 A Neeman, The connection between the K–theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel, Ann. Sci. École Norm. Sup. 25 (1992) 547 MR1191736
59 A Neeman, The Grothendieck duality theorem via Bousfield’s techniques and Brown representability, J. Amer. Math. Soc. 9 (1996) 205 MR1308405
60 R Nest, B Tsygan, Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems, Asian J. Math. 5 (2001) 599 MR1913813
61 R Nest, B Tsygan, Remarks on modules over deformation quantization algebras, Mosc. Math. J. 4 (2004) 911 MR2124172
62 C Pedrini, C Weibel, The higher K–theory of a complex surface, Compositio Math. 129 (2001) 239 MR1868355
63 F Petit, DG affinity of DQ-modules, Int. Math. Res. Not. 2012 (2012) 1414 MR2899956
64 A Premet, Special transverse slices and their enveloping algebras, Adv. Math. 170 (2002) 1 MR1929302
65 D Quillen, Higher algebraic K–theory, I, from: "Algebraic K–theory, I : Higher K–theories" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85 MR0338129
66 W Soergel, The Hochschild cohomology ring of regular maximal primitive quotients of enveloping algebras of semisimple Lie algebras, Ann. Sci. École Norm. Sup. 29 (1996) 535 MR1386225
67 M Van den Bergh, A relation between Hochschild homology and cohomology for Gorenstein rings, Proc. Amer. Math. Soc. 126 (1998) 1345 MR1443171
68 F Van Oystaeyen, R Sallam, A microstructure sheaf and quantum sections over a projective scheme, J. Algebra 158 (1993) 201 MR1223674
69 B Webster, Centers of KLR algebras and cohomology rings of quiver varieties, preprint (2015) arXiv:1504:04401
70 M Wodzicki, Cyclic homology of differential operators, Duke Math. J. 54 (1987) 641 MR899408
71 A Yekutieli, On flatness and completion for infinitely generated modules over Noetherian rings, Comm. Algebra 39 (2011) 4221 MR2855123