Geometry & Topology Volume 24, issue 5 (2020)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Equivariant Hodge theory and noncommutative geometry

Daniel Halpern-Leistner and Daniel Pomerleano

Geometry & Topology 24 (2020) 2361–2433

DOI: 10.2140/gt.2020.24.2361

Bibliography

1	M F Atiyah, G B Segal, Equivariant K–theory and completion, J. Differential Geom. 3 (1969) 1 MR259946
2	V Baranovsky, Orbifold cohomology as periodic cyclic homology, Int. J. Math. 14 (2003) 791 MR2013145
3	P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
4	D Ben-Zvi, J Francis, D Nadler, Integral transforms and Drinfeld centers in derived algebraic geometry, J. Amer. Math. Soc. 23 (2010) 909 MR2669705
5	D Ben-Zvi, D Nadler, A Preygel, Integral transforms for coherent sheaves, J. Eur. Math. Soc. 19 (2017) 3763 MR3730514
6	D Bergh, Functorial destackification of tame stacks with abelian stabilisers, Compos. Math. 153 (2017) 1257 MR3705256
7	D Bergh, V A Lunts, O M Schnürer, Geometricity for derived categories of algebraic stacks, Selecta Math. 22 (2016) 2535 MR3573964
8	A Blanc, Topological K–theory of complex noncommutative spaces, Compos. Math. 152 (2016) 489 MR3477639
9	A Blanc, M Robalo, B Toën, G Vezzosi, Motivic realizations of singularity categories and vanishing cycles, J. Éc. Polytech. Math. 5 (2018) 651 MR3877165
10	J Block, E Getzler, Equivariant cyclic homology and equivariant differential forms, Ann. Sci. École Norm. Sup. 27 (1994) 493 MR1290397
11	A J Blumberg, D Gepner, G Tabuada, A universal characterization of higher algebraic K–theory, Geom. Topol. 17 (2013) 733 MR3070515
12	D C Cisinski, F Déglise, Étale motives, Compos. Math. 152 (2016) 556 MR3477640
13	L Cohn, Differential graded categories are k–linear stable infinity categories, preprint (2013) arXiv:1308.2587
14	A Căldăraru, J Tu, Curved A_∞ algebras and Landau–Ginzburg models, New York J. Math. 19 (2013) 305 MR3084707
15	P Deligne, Théorie de Hodge, III, Inst. Hautes Études Sci. Publ. Math. 44 (1974) 5 MR498552
16	V Drinfeld, D Gaitsgory, On some finiteness questions for algebraic stacks, Geom. Funct. Anal. 23 (2013) 149 MR3037900
17	T Dyckerhoff, Compact generators in categories of matrix factorizations, Duke Math. J. 159 (2011) 223 MR2824483
18	A I Efimov, Cyclic homology of categories of matrix factorizations, Int. Math. Res. Not. 2018 (2018) 3834 MR3815168
19	A I Efimov, L Positselski, Coherent analogues of matrix factorizations and relative singularity categories, Algebra Number Theory 9 (2015) 1159 MR3366002
20	D S Freed, M J Hopkins, C Teleman, Twisted equivariant K–theory with complex coefficients, J. Topol. 1 (2008) 16 MR2365650
21	D Gaitsgory, Ind-coherent sheaves, Mosc. Math. J. 13 (2013) 399 MR3136100
22	D Gaitsgory, N Rozenblyum, A study in derived algebraic geometry, I : Correspondences and duality, 221, Amer. Math. Soc. (2017) MR3701352
23	J Hall, D Rydh, Perfect complexes on algebraic stacks, Compos. Math. 153 (2017) 2318 MR3705292
24	D Halpern-Leistner, The derived category of a GIT quotient, J. Amer. Math. Soc. 28 (2015) 871 MR3327537
25	D Halpern-Leistner, Remarks on Θ–stratifications and derived categories, preprint (2015) arXiv:1502.03083
26	D Halpern-Leistner, A Preygel, Mapping stacks and categorical notions of properness, preprint (2014) arXiv:1402.3204
27	W H Hesselink, Uniform instability in reductive groups, J. Reine Angew. Math. 303-304 (1978) 74 MR514673
28	Y Hirano, Derived Knörrer periodicity and Orlov’s theorem for gauged Landau–Ginzburg models, Compos. Math. 153 (2017) 973 MR3631231
29	A Ishii, K Ueda, The special McKay correspondence and exceptional collections, Tohoku Math. J. 67 (2015) 585 MR3436544
30	M U Isik, Equivalence of the derived category of a variety with a singularity category, Int. Math. Res. Not. 2013 (2013) 2787 MR3071664
31	D Kaledin, Non-commutative Hodge-to-de Rham degeneration via the method of Deligne–Illusie, Pure Appl. Math. Q. 4 (2008) 785 MR2435845
32	D Kaledin, Spectral sequences for cyclic homology, from: "Algebra, geometry, and physics in the 21st century" (editors D Auroux, L Katzarkov, T Pantev, Y Soibelman, Y Tschinkel), Progr. Math. 324, Birkhäuser (2017) 99 MR3702384
33	L Katzarkov, M Kontsevich, T Pantev, Hodge theoretic aspects of mirror symmetry, from: "From Hodge theory to integrability and TQFT tt^∗–geometry" (editors R Y Donagi, K Wendland), Proc. Sympos. Pure Math. 78, Amer. Math. Soc. (2008) 87 MR2483750
34	L Katzarkov, M Kontsevich, T Pantev, Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models, J. Differential Geom. 105 (2017) 55 MR3592695
35	B Keller, On differential graded categories, from: "International Congress of Mathematicians, II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 151 MR2275593
36	F C Kirwan, Cohomology of quotients in symplectic and algebraic geometry, 31, Princeton Univ. Press (1984) MR766741
37	F C Kirwan, Partial desingularisations of quotients of nonsingular varieties and their Betti numbers, Ann. of Math. 122 (1985) 41 MR799252
38	M Kontsevich, Y Soibelman, Notes on A_∞–algebras, A_∞–categories and non-commutative geometry, from: "Homological mirror symmetry" (editors A Kapustin, M Kreuzer, K G Schlesinger), Lecture Notes in Phys. 757, Springer (2009) 153 MR2596638
39	A Kresch, On the geometry of Deligne–Mumford stacks, from: "Algebraic geometry, I" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 259 MR2483938
40	G Laumon, L Moret-Bailly, Champs algébriques, 39, Springer (2000) MR1771927
41	M Levine, F Morel, Algebraic cobordism, Springer (2007) MR2286826
42	L G Lewis Jr., J P May, M Steinberger, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
43	K H Lin, D Pomerleano, Global matrix factorizations, Math. Res. Lett. 20 (2013) 91 MR3126725
44	J L Loday, Cyclic homology, 301, Springer (1992) MR1217970
45	J Lurie, Derived algebraic geometry, VII: Spectral schemes, preprint (2011)
46	J Lurie, Higher algebra, preprint (2017)
47	J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
48	B Mitchell, Rings with several objects, Adv. Math. 8 (1972) 1 MR294454
49	F Morel, V Voevodsky, 𝔸¹–homotopy theory of schemes, Inst. Hautes Études Sci. Publ. Math. 90 (1999) 45 MR1813224
50	L Ness, A stratification of the null cone via the moment map, Amer. J. Math. 106 (1984) 1281 MR765581
51	B Noohi, Homotopy types of topological stacks, Adv. Math. 230 (2012) 2014 MR2927363
52	A Ogus, V Vologodsky, Nonabelian Hodge theory in characteristic p, Publ. Math. Inst. Hautes Études Sci. 106 (2007) 1 MR2373230
53	M C Olsson, On proper coverings of Artin stacks, Adv. Math. 198 (2005) 93 MR2183251
54	D Orlov, Matrix factorizations for nonaffine LG–models, Math. Ann. 353 (2012) 95 MR2910782
55	A Preygel, Thom–Sebastiani and duality for matrix factorizations, preprint (2011) arXiv:1101.5834
56	K Saito, Period mapping associated to a primitive form, Publ. Res. Inst. Math. Sci. 19 (1983) 1231 MR723468
57	M Satriano, de Rham theory for tame stacks and schemes with linearly reductive singularities, Ann. Inst. Fourier (Grenoble) 62 (2012) 2013 MR3060750
58	E Segal, The closed state space of affine Landau–Ginzburg B–models, J. Noncommut. Geom. 7 (2013) 857 MR3108698
59	G Segal, Equivariant K–theory, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 129 MR234452
60	D Shklyarov, Non-commutative Hodge structures : towards matching categorical and geometric examples, Trans. Amer. Math. Soc. 366 (2014) 2923 MR3180736
61	J H M Steenbrink, Mixed Hodge structure on the vanishing cohomology, from: "Real and complex singularities" (editor P Holm), Sijthoff & Noordhoff (1977) 525 MR0485870
62	G Tabuada, Higher K–theory via universal invariants, Duke Math. J. 145 (2008) 121 MR2451292
63	C Teleman, The quantization conjecture revisited, Ann. of Math. 152 (2000) 1 MR1792291
64	R W Thomason, Riemann–Roch for algebraic versus topological K–theory, J. Pure Appl. Algebra 27 (1983) 87 MR680887
65	R W Thomason, Algebraic K–theory of group scheme actions, from: "Algebraic topology and algebraic K–theory" (editor W Browder), Ann. of Math. Stud. 113, Princeton Univ. Press (1987) 539 MR921490
66	R W Thomason, Equivariant algebraic vs. topological K–homology Atiyah–Segal-style, Duke Math. J. 56 (1988) 589 MR948534
67	B Toën, Théorèmes de Riemann–Roch pour les champs de Deligne–Mumford, K–Theory 18 (1999) 33 MR1710187