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Brauer groups and étale cohomology in derived algebraic geometry

Benjamin Antieau and David Gepner

Geometry & Topology 18 (2014) 1149–1244
1 M Ando, A J Blumberg, D Gepner, Parameterized spectra, multiplicative Thom spectra, and the twisted Umkehr map, arXiv:1112.2203
2 B Antieau, D Gepner, J M Gómez, Actions of Eilenberg–Mac Lane spaces on $K$–theory spectra and uniqueness of twisted $K$–theory, to appear in Trans. Amer. Math. Soc.
3 D Arinkin, D Gaitsgory, Singular support of coherent sheaves, and the geometric Langlands conjecture, arXiv:1201.6343
4 M Artin, D Mumford, Some elementary examples of unirational varieties which are not rational, Proc. London Math. Soc. (3) 25 (1972) 75 MR0321934
5 M Auslander, O Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960) 367 MR0121392
6 G Azumaya, On maximally central algebras, Nagoya Math. J. 2 (1951) 119 MR0040287
7 A Baker, A Lazarev, Topological Hochschild cohomology and generalized Morita equivalence, Algebr. Geom. Topol. 4 (2004) 623 MR2100675
8 A Baker, B Richter, M Szymik, Brauer groups for commutative $S$–algebras, J. Pure Appl. Algebra 216 (2012) 2361 MR2927172
9 D Ben-Zvi, J Francis, D Nadler, Integral transforms and Drinfeld centers in derived algebraic geometry, J. Amer. Math. Soc. 23 (2010) 909 MR2669705
10 M Van den Bergh, Three-dimensional flops and noncommutative rings, Duke Math. J. 122 (2004) 423 MR2057015
11 P Berthelot, A Grothendieck, L Illusie, Théorie des intersections et théorème de Riemann–Roch, Lecture Notes in Math. 225, Springer (1971) MR0354655
12 A J Blumberg, D Gepner, G Tabuada, A universal characterization of higher algebraic $K$–theory, Geom. Topol. 17 (2013) 733 MR3070515
13 M Bökstedt, A Neeman, Homotopy limits in triangulated categories, Compositio Math. 86 (1993) 209 MR1214458
14 A Bondal, M van den Bergh, Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J. 3 (2003) 1, 258 MR1996800
15 F Borceux, E Vitale, Azumaya categories, Appl. Categ. Structures 10 (2002) 449 MR1937232
16 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer (1972) MR0365573
17 K S Brown, S M Gersten, Algebraic $K\!$–theory as generalized sheaf cohomology, from: "Algebraic $K\!$–theory, I: Higher $K\!$–theories", Lecture Notes in Math. 341, Springer (1973) 266 MR0347943
18 D C Cisinski, G Tabuada, Symmetric monoidal structure on non-commutative motives, J. $K$–Theory 9 (2012) 201 MR2922389
19 F R DeMeyer, The Brauer group of affine curves, from: "Brauer groups", Springer (1976) 16 MR0437537
20 C Deninger, A proper base change theorem for nontorsion sheaves in étale cohomology, J. Pure Appl. Algebra 50 (1988) 231 MR938616
21 J W Duskin, The Azumaya complex of a commutative ring, from: "Categorical algebra and its applications" (editor F Borceux), Lecture Notes in Math. 1348, Springer (1988) 107 MR975963
22 D Edidin, B Hassett, A Kresch, A Vistoli, Brauer groups and quotient stacks, Amer. J. Math. 123 (2001) 761 MR1844577
23 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs 47, Amer. Math. Soc. (1997) MR1417719
24 H Fausk, Picard groups of derived categories, J. Pure Appl. Algebra 180 (2003) 251 MR1966659
25 O Gabber, Some theorems on Azumaya algebras, from: "The Brauer group" (editors M Kervaire, M Ojanguren), Lecture Notes in Math. 844, Springer (1981) 129 MR611868
26 D Gepner, T Lawson, Brauer groups and Galois cohomology of commutative ring spectra, in preparation
27 P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Mathematics 174, Birkhäuser (1999) MR1711612
28 R Gordon, A J Power, R Street, Coherence for tricategories, Mem. Amer. Math. Soc. 558 (1995) MR1261589
29 A Grothendieck, Éléments de géométrie algébrique, I: Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. (1960) 228 MR0217083
30 A Grothendieck, Éléments de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas IV, Inst. Hautes Études Sci. Publ. Math. (1967) 361 MR0238860
31 A Grothendieck, Le groupe de Brauer, I: Algèbres d'Azumaya et interprétations diverses, from: "Dix exposés sur la cohomologie des schémas", North-Holland (1968) 46 MR0244269
32 A Grothendieck, Le groupe de Brauer, II: Théorie cohomologique, from: "Dix exposés sur la cohomologie des schémas", North-Holland (1968) 67 MR0244270
33 A Grothendieck, Le groupe de Brauer, III: Exemples et compléments, from: "Dix exposés sur la cohomologie des schémas", North-Holland (1968) 88 MR0244271
34 M J Hopkins, M Mahowald, H Sadofsky, Constructions of elements in Picard groups, from: "Topology and representation theory" (editors E M Friedlander, M E Mahowald), Contemp. Math. 158, Amer. Math. Soc. (1994) 89 MR1263713
35 N Johnson, Azumaya objects in triangulated bicategories, to appear in Journal of Homotopy and Related Structures
36 A J de Jong, A result of Gabber, preprint
37 M Kapranov, Noncommutative geometry based on commutator expansions, J. Reine Angew. Math. 505 (1998) 73 MR1662244
38 A Lazarev, Homotopy theory of $A_\infty$ ring spectra and applications to $M\mathrm{U}$–modules, $K$–Theory 24 (2001) 243 MR1876800
39 M Lieblich, Moduli of twisted sheaves and generalized Azumaya algebras, PhD thesis, Mass. Inst. of Tech. (2004)
40 J Lurie, Derived algebraic geometry, PhD thesis, Mass. Inst. of Tech. (2004)
41 J Lurie, Higher topos theory, Annals of Mathematics Studies 170, Princeton Univ. Press (2009) MR2522659
42 J Lurie, Derived algebraic geometry VII: Spectral schemes (2011)
43 J Lurie, Derived algebraic geometry XI: Descent theorems (2011)
44 J Lurie, Derived algebraic geometry XIV: Representability theorems (2012)
45 J Lurie, Higher algebra (2012)
46 H Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics 8, Cambridge Univ. Press (1989) MR1011461
47 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
48 A Neeman, The Grothendieck duality theorem via Bousfield's techniques and Brown representability, J. Amer. Math. Soc. 9 (1996) 205 MR1308405
49 P Pandit, Moduli problems in derived noncommutative geometry, PhD thesis, University of Pennsylvania (2011)
50 S Schwede, The stable homotopy category is rigid, Ann. of Math. 166 (2007) 837 MR2373374
51 S Schwede, B Shipley, A uniqueness theorem for stable homotopy theory, Math. Z. 239 (2002) 803 MR1902062
52 S Schwede, B Shipley, Stable model categories are categories of modules, Topology 42 (2003) 103 MR1928647
53 C Simpson, Algebraic (geometric) $n$–stacks, arXiv:absalg-geom/9609014
54 M Szymik, Brauer spaces for commutative rings and structured ring spectra, arXiv:1110.2956
55 R W Thomason, The classification of triangulated subcategories, Compositio Math. 105 (1997) 1 MR1436741
56 R W Thomason, T Trobaugh, Higher algebraic $K\!$–theory of schemes and of derived categories, from: "The Grothendieck Festschrift, Vol. III" (editors P Cartier, L Illusie, N M Katz, G Laumon, K A Ribet), Progr. Math. 88, Birkhäuser (1990) 247 MR1106918
57 B Toën, Derived Azumaya algebras and generators for twisted derived categories, Invent. Math. 189 (2012) 581 MR2957304
58 B Toën, M Vaquié, Moduli of objects in dg–categories, Ann. Sci. École Norm. Sup. 40 (2007) 387 MR2493386
59 B Toën, G Vezzosi, Homotopical algebraic geometry, II: Geometric stacks and applications, Mem. Amer. Math. Soc. 193 (2008) MR2394633
60 E M Vitale, The Brauer and Brauer–Taylor groups of a symmetric monoidal category, Cahiers Topologie Géom. Différentielle Catég. 37 (1996) 91 MR1394505