Volume 23, issue 2 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Derived induction and restriction theory

Akhil Mathew, Niko Naumann and Justin Noel

Geometry & Topology 23 (2019) 541–636
1 J F Adams, Prerequisites (on equivariant stable homotopy) for Carlsson’s lecture, from: "Algebraic topology, Aarhus 1982" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 483 MR764596
2 A Adem, R J Milgram, Cohomology of finite groups, 309, Springer (2004) MR2035696
3 D W Anderson, E H Brown Jr., F P Peterson, The structure of the Spin cobordism ring, Ann. of Math. 86 (1967) 271 MR0219077
4 M Ando, M Hopkins, C Rezk, Multiplicative orientations of KO–theory and of the spectrum of topological modular forms, preprint (2006)
5 V Angeltveit, Topological Hochschild homology and cohomology of A ring spectra, Geom. Topol. 12 (2008) 987 MR2403804
6 M F Atiyah, Characters and cohomology of finite groups, Inst. Hautes Études Sci. Publ. Math. 9 (1961) 23 MR0148722
7 M F Atiyah, K–theory and reality, Quart. J. Math. Oxford Ser. 17 (1966) 367 MR0206940
8 M F Atiyah, Bott periodicity and the index of elliptic operators, Quart. J. Math. Oxford Ser. 19 (1968) 113 MR0228000
9 M F Atiyah, I G Macdonald, Introduction to commutative algebra, Addison-Wesley (1969) MR0242802
10 M F Atiyah, G B Segal, Equivariant K–theory and completion, J. Differential Geometry 3 (1969) 1 MR0259946
11 P Balmer, Descent in triangulated categories, Math. Ann. 353 (2012) 109 MR2910783
12 P Balmer, Separable extensions in tensor-triangular geometry and generalized Quillen stratification, Ann. Sci. Éc. Norm. Supér. 49 (2016) 907 MR3552016
13 P Balmer, I Dell’Ambrogio, B Sanders, Restriction to finite-index subgroups as étale extensions in topology, KK–theory and geometry, Algebr. Geom. Topol. 15 (2015) 3025 MR3426702
14 D Barnes, Splitting monoidal stable model categories, J. Pure Appl. Algebra 213 (2009) 846 MR2494375
15 C Barwick, Spectral Mackey functors and equivariant algebraic K–theory, I, Adv. Math. 304 (2017) 646 MR3558219
16 C Barwick, S Glasman, J Shah, Spectral Mackey functors and equivariant algebraic K–theory, II, preprint (2015) arXiv:1505.03098
17 M Behrens, The construction of tmf, from: "Topological modular forms" (editors C L Douglas, J Francis, A G Henriques, M A Hill), Mathematical Surveys and Monographs 201, Amer. Math. Soc. (2014) 131 MR3223024
18 J M Boardman, Conditionally convergent spectral sequences, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 49 MR1718076
19 A Bojanowska, S Jackowski, A spectral sequence convergent to equivariant K–theory, from: "Topology symposium, Siegen 1979" (editors U Koschorke, W D Neumann), Lecture Notes in Math. 788, Springer (1980) 245 MR585662
20 A K Bousfield, Homotopy spectral sequences and obstructions, Israel J. Math. 66 (1989) 54 MR1017155
21 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
22 G E Bredon, Equivariant cohomology theories, 34, Springer (1967) MR0214062
23 T Bröcker, E C Hook, Stable equivariant bordism, Math. Z. 129 (1972) 269 MR0321119
24 J F Carlson, Cohomology and induction from elementary abelian subgroups, Q. J. Math. 51 (2000) 169 MR1765788
25 G Carlsson, Equivariant stable homotopy and Segal’s Burnside ring conjecture, Ann. of Math. 120 (1984) 189 MR763905
26 H Cartan, S Eilenberg, Homological algebra, Princeton Univ. Press (1956) MR0077480
27 S R Costenoble, An introduction to equivariant cobordism MR1413302
28 T tom Dieck, Bordism of G–manifolds and integrality theorems, Topology 9 (1970) 345 MR0266241
29 T tom Dieck, Transformation groups, 8, de Gruyter (1987) MR889050
30 A W M Dress, Contributions to the theory of induced representations, from: "Algebraic K–theory, II : ‘Classical’ algebraic K–theory and connections with arithmetic" (editor H Bass), Lecture Notes in Math. 342, Springer (1973) 183 MR0384917
31 A W M Dress, Induction and structure theorems for orthogonal representations of finite groups, Ann. of Math. 102 (1975) 291 MR0387392
32 D. Dugger, A primer on homotopy colimits, book project (2008)
33 W G Dwyer, Homology decompositions for classifying spaces of finite groups, Topology 36 (1997) 783 MR1432421
34 W G Dwyer, Sharp homology decompositions for classifying spaces of finite groups, from: "Group representations: cohomology, group actions and topology" (editors A Adem, J Carlson, S Priddy, P Webb), Proc. Sympos. Pure Math. 63, Amer. Math. Soc. (1998) 197 MR1603159
35 W G Dwyer, J P C Greenlees, Complete modules and torsion modules, Amer. J. Math. 124 (2002) 199 MR1879003
36 L Fajstrup, Tate cohomology of periodic K–theory with reality is trivial, Trans. Amer. Math. Soc. 347 (1995) 1841 MR1273490
37 H Fausk, Generalized Artin and Brauer induction for compact Lie groups, Trans. Amer. Math. Soc. 360 (2008) 5043 MR2403712
38 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
39 J A Green, Axiomatic representation theory for finite groups, J. Pure Appl. Algebra 1 (1971) 41 MR0279208
40 J P C Greenlees, Homotopy equivariance, strict equivariance and induction theory, Proc. Edinburgh Math. Soc. 35 (1992) 473 MR1187009
41 J P C Greenlees, Equivariant connective K–theory for compact Lie groups, J. Pure Appl. Algebra 187 (2004) 129 MR2027899
42 J P C Greenlees, Equivariant versions of real and complex connective K–theory, Homology Homotopy Appl. 7 (2005) 63 MR2205170
43 J P C Greenlees, J P May, Completions in algebra and topology, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 255 MR1361892
44 J P C Greenlees, J P May, Generalized Tate cohomology, 543, Amer. Math. Soc. (1995) MR1230773
45 J P C Greenlees, J P May, Localization and completion theorems for MU–module spectra, Ann. of Math. 146 (1997) 509 MR1491447
46 J P C Greenlees, H Sadofsky, The Tate spectrum of vn–periodic complex oriented theories, Math. Z. 222 (1996) 391 MR1400199
47 J P C Greenlees, N P Strickland, Varieties and local cohomology for chromatic group cohomology rings, Topology 38 (1999) 1093 MR1688422
48 J Grodal, Higher limits via subgroup complexes, Ann. of Math. 155 (2002) 405 MR1906592
49 J Grodal, S D Smith, Propagating sharp group homology decompositions, Adv. Math. 200 (2006) 525 MR2200855
50 B Guillou, J P May, Models of G–spectra as presheaves of spectra, preprint (2011) arXiv:1110.3571
51 M A Hill, M J Hopkins, D C Ravenel, The Arf–Kervaire problem in algebraic topology : sketch of the proof, from: "Current developments in mathematics, 2010" (editors D Jerison, B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), Int. (2011) 1 MR2906370
52 M A Hill, M J Hopkins, D C Ravenel, On the nonexistence of elements of Kervaire invariant one, Ann. of Math. 184 (2016) 1 MR3505179
53 M J Hopkins, Global methods in homotopy theory, from: "Homotopy theory" (editors E Rees, J D S Jones), London Math. Soc. Lecture Note Ser. 117, Cambridge Univ. Press (1987) 73 MR932260
54 M J Hopkins, N J Kuhn, D C Ravenel, Generalized group characters and complex oriented cohomology theories, J. Amer. Math. Soc. 13 (2000) 553 MR1758754
55 M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, II, Ann. of Math. 148 (1998) 1 MR1652975
56 M A Hovey, D C Ravenel, The 7–connected cobordism ring at p = 3, Trans. Amer. Math. Soc. 347 (1995) 3473 MR1297530
57 D Husemoller, Fibre bundles, 20, Springer (1994) MR1249482
58 D Husemöller, M Joachim, B Jurčo, M Schottenloher, Basic bundle theory and K–cohomology invariants, 726, Springer (2008) MR2377868
59 S Illman, The equivariant triangulation theorem for actions of compact Lie groups, Math. Ann. 262 (1983) 487 MR696520
60 S Jackowski, J McClure, Homotopy decomposition of classifying spaces via elementary abelian subgroups, Topology 31 (1992) 113 MR1153240
61 N J Kuhn, Tate cohomology and periodic localization of polynomial functors, Invent. Math. 157 (2004) 345 MR2076926
62 P S Landweber, Conjugations on complex manifolds and equivariant homotopy of MU, Bull. Amer. Math. Soc. 74 (1968) 271 MR0222890
63 L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
64 W Lück, Survey on classifying spaces for families of subgroups, from: "Infinite groups: geometric, combinatorial and dynamical aspects" (editors L Bartholdi, T Ceccherini-Silberstein, T Smirnova-Nagnibeda, A Zuk), Progr. Math. 248, Birkhäuser (2005) 269 MR2195456
65 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
66 J Lurie, Derived algebraic geometry, XII : Proper morphisms, completions, and the Grothendieck existence theorem, preprint (2011)
67 J. Lurie, Higher algebra, book project (2014)
68 M A Mandell, Equivariant symmetric spectra, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 399 MR2066508
69 M A Mandell, The smash product for derived categories in stable homotopy theory, Adv. Math. 230 (2012) 1531 MR2927347
70 M A Mandell, J P May, Equivariant orthogonal spectra and S–modules, 755, Amer. Math. Soc. (2002) MR1922205
71 A Mathew, A thick subcategory theorem for modules over certain ring spectra, Geom. Topol. 19 (2015) 2359 MR3375530
72 A Mathew, The homology of tmf, Homology Homotopy Appl. 18 (2016) 1 MR3515195
73 A Mathew, N Naumann, J Noel, Nilpotence and descent in equivariant stable homotopy theory, Adv. Math. 305 (2017) 994 MR3570153
74 A Mathew, V Stojanoska, The Picard group of topological modular forms via descent theory, Geom. Topol. 20 (2016) 3133 MR3590352
75 J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
76 J P May, J E McClure, A reduction of the Segal conjecture, from: "Current trends in algebraic topology, II" (editors R M Kane, S O Kochman, P S Selick, V P Snaith), CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 209 MR686147
77 D Nardin, Parametrized higher category theory and higher algebra, Exposé IV : Stability with respect to an orbital –category, preprint (2016) arXiv:1608.07704
78 D Quillen, The spectrum of an equivariant cohomology ring, I, Ann. of Math. 94 (1971) 549 MR0298694
79 D Quillen, The spectrum of an equivariant cohomology ring, II, Ann. of Math. 94 (1971) 573 MR0298694
80 D C Ravenel, Nilpotence and periodicity in stable homotopy theory, 128, Princeton Univ. Press (1992) MR1192553
81 Y B Rudyak, On Thom spectra, orientability, and cobordism, Springer (1998) MR1627486
82 G Segal, The representation ring of a compact Lie group, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 113 MR0248277
83 J P Serre, Linear representations of finite groups, 42, Springer (1977) MR0450380
84 J H Silverman, The arithmetic of elliptic curves, 106, Springer (1986) MR817210
85 J Smith, Finite complexes with vanishing lines of small slope, preprint (2005)
86 R E Stong, Notes on cobordism theory, Princeton Univ. Press (1968) MR0248858
87 C T C Wall, Determination of the cobordism ring, Ann. of Math. 72 (1960) 292 MR0120654
88 S Waner, Mackey functors and G–cohomology, Proc. Amer. Math. Soc. 90 (1984) 641 MR733419
89 P Webb, A guide to Mackey functors, from: "Handbook of algebra, II" (editor M Hazewinkel), North-Holland (2000) 805 MR1759612