Geometry & Topology Volume 22, issue 5 (2018)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Additive invariants of orbifolds

Gonçalo Tabuada and Michel Van den Bergh

Geometry & Topology 22 (2018) 3003–3048

DOI: 10.2140/gt.2018.22.3003

Bibliography

1	A Adem, Y Ruan, Twisted orbifold K–theory, Comm. Math. Phys. 237 (2003) 533 MR1993337
2	Y André, Une introduction aux motifs (motifs purs, motifs mixtes, périodes), 17, Soc. Math. France (2004) MR2115000
3	D Arinkin, A Caldararu, M Hablicsek, Formality of derived intersections and the orbifold HKR isomorphism, preprint (2014) arXiv:1412.5233
4	V Baranovsky, Orbifold cohomology as periodic cyclic homology, Internat. J. Math. 14 (2003) 791 MR2013145
5	V Baranovsky, T Petrov, Brauer groups and crepant resolutions, Adv. Math. 209 (2007) 547 MR2296308
6	M Bernardara, M Marcolli, G Tabuada, Some remarks concerning Voevodsky’s nilpotence conjecture, J. Reine Angew. Math. (2015)
7	R V Bezrukavnikov, D B Kaledin, McKay equivalence for symplectic resolutions of quotient singularities, Tr. Mat. Inst. Steklova 246 (2004) 20 MR2101282
8	A Bondal, M van den Bergh, Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J. 3 (2003) 1 MR1996800
9	A Bondal, D Orlov, Semiorthogonal decomposition for algebraic varieties, preprint (2000) arXiv:alg-geom/9506012
10	A Bondal, D Orlov, Derived categories of coherent sheaves, from: "Proceedings of the International Congress of Mathematicians" (editor L Tatsien), Higher Ed. (2002) 47 MR1957019
11	T Bridgeland, A King, M Reid, The McKay correspondence as an equivalence of derived categories, J. Amer. Math. Soc. 14 (2001) 535 MR1824990
12	W Chen, Y Ruan, A new cohomology theory of orbifold, Comm. Math. Phys. 248 (2004) 1 MR2104605
13	C W Curtis, I Reiner, Representation theory of finite groups and associative algebras, XI, Interscience (1962) MR0144979
14	A Cǎldǎraru, Hochschild–Kostant–Rosenberg isomorphism for orbifolds, talk at “Interacting algebraic geometry” conference, Dijon (2016)
15	T tom Dieck, Transformation groups and representation theory, 766, Springer (1979) MR551743
16	B L Feĭgin, B L Tsygan, Additive K–theory, from: "K–theory, arithmetic and geometry" (editor Y I Manin), Lecture Notes in Math. 1289, Springer (1987) 67 MR923136
17	W Fulton, S Lang, Riemann–Roch algebra, 277, Springer (1985) MR801033
18	H Gillet, K–theory and intersection theory, from: "Handbook of K–theory" (editors E M Friedlander, D R Grayson), Springer (2005) 235 MR2181825
19	H Gillet, C Soulé, Descent, motives and K–theory, J. Reine Angew. Math. 478 (1996) 127 MR1409056
20	A Grothendieck, Standard conjectures on algebraic cycles, from: "Algebraic geometry", Oxford Univ. Press (1969) 193 MR0268189
21	J Hall, D Rydh, Algebraic groups and compact generation of their derived categories of representations, Indiana Univ. Math. J. 64 (2015) 1903 MR3436239
22	D Halpern-Leistner, D Pomerleano, Equivariant Hodge theory and noncommutative geometry, preprint (2015) arXiv:1507.01924
23	L Hesselholt, Topological Hochschild homology and the Hasse–Weil zeta function, preprint (2016) arXiv:1602.01980
24	A J d Jong, The stacks project, electronic resource (2014)
25	B Kahn, R Sebastian, Smash-nilpotent cycles on abelian 3–folds, Math. Res. Lett. 16 (2009) 1007 MR2576688
26	M Kapranov, E Vasserot, Kleinian singularities, derived categories and Hall algebras, Math. Ann. 316 (2000) 565 MR1752785
27	Y Kawamata, D–equivalence and K–equivalence, J. Differential Geom. 61 (2002) 147 MR1949787
28	S Keel, S Mori, Quotients by groupoids, Ann. of Math. 145 (1997) 193 MR1432041
29	B Keller, On the cyclic homology of ringed spaces and schemes, Doc. Math. 3 (1998) 231 MR1647519
30	B Keller, On the cyclic homology of exact categories, J. Pure Appl. Algebra 136 (1999) 1 MR1667558
31	B Keller, On differential graded categories, from: "International Congress of Mathematicians" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 151 MR2275593
32	S L Kleiman, Algebraic cycles and the Weil conjectures, from: "Dix exposés sur la cohomologie des schémas", Adv. Stud. Pure Math. 3, North-Holland (1968) 359 MR292838
33	S L Kleiman, The standard conjectures, from: "Motives" (editors U Jannsen, S Kleiman, J P Serre), Proc. Sympos. Pure Math. 55, Amer. Math. Soc. (1994) 3 MR1265519
34	M Kontsevich, Noncommutative motives, seminar talk (2005)
35	M Kontsevich, Notes on motives in finite characteristic, from: "Algebra, arithmetic, and geometry : in honor of Yu I Manin, II" (editors Y Tschinkel, Y Zarhin), Progr. Math. 270, Birkhäuser (2009) 213 MR2641191
36	M Kontsevich, Mixed noncommutative motives, conference talk, from “Workshop on homological mirror symmetry”, Miami (2010)
37	N J Kuhn, Character rings in algebraic topology, from: "Advances in homotopy theory" (editors S M Salamon, B Steer, W A Sutherland), London Math. Soc. Lecture Note Ser. 139, Cambridge Univ. Press (1989) 111 MR1055872
38	D I Lieberman, Numerical and homological equivalence of algebraic cycles on Hodge manifolds, Amer. J. Math. 90 (1968) 366 MR0230336
39	V A Lunts, D O Orlov, Uniqueness of enhancement for triangulated categories, J. Amer. Math. Soc. 23 (2010) 853 MR2629991
40	J I Manin, Correspondences, motifs and monoidal transformations, Mat. Sb. 77(119) (1968) 475 MR0258836
41	C Năstăsescu, F van Oystaeyen, Graded ring theory, 28, North-Holland (1982) MR676974
42	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
43	A Polishchuk, M Van den Bergh, Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups, preprint (2015) arXiv:1503.04160
44	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
45	O M Schnürer, Six operations on dg enhancements of derived categories of sheaves, preprint (2015) arXiv:1507.08697
46	G Tabuada, Galois descent of additive invariants, Bull. Lond. Math. Soc. 46 (2014) 385 MR3194756
47	G Tabuada, Noncommutative motives, 63, Amer. Math. Soc. (2015) MR3379910
48	G Tabuada, Recent developments on noncommutative motives, preprint (2016) arXiv:1611.05439
49	G Tabuada, A note on Grothendieck’s standard conjectures of type C⁺ and D, Proc. Amer. Math. Soc. 146 (2018) 1389 MR3754327
50	G Tabuada, M Van den Bergh, Noncommutative motives of Azumaya algebras, J. Inst. Math. Jussieu 14 (2015) 379 MR3315059
51	G Tabuada, M Van den Bergh, The Gysin triangle via localization and A¹–homotopy invariance, Trans. Amer. Math. Soc. 370 (2018) 421 MR3717985
52	B Toen, Théorèmes de Riemann–Roch pour les champs de Deligne–Mumford, K-Theory 18 (1999) 33 MR1710187
53	C Vafa, E Witten, On orbifolds with discrete torsion, J. Geom. Phys. 15 (1995) 189 MR1316330
54	A Vistoli, Higher equivariant K–theory for finite group actions, Duke Math. J. 63 (1991) 399 MR1115114
55	V Voevodsky, A nilpotence theorem for cycles algebraically equivalent to zero, Internat. Math. Res. Notices 1995 (1995) 187 MR1326064
56	C Voisin, Remarks on zero-cycles of self-products of varieties, from: "Moduli of vector bundles" (editor M Maruyama), Lecture Notes in Pure and Appl. Math. 179, Dekker (1996) 265 MR1397993