Algebraic & Geometric Topology Volume 17, issue 4 (2017)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

The $C_2$–spectrum $\mathrm{Tmf}_1(3)$ and its invertible modules

Michael A Hill and Lennart Meier

Algebraic & Geometric Topology 17 (2017) 1953–2011

DOI: 10.2140/agt.2017.17.1953

Bibliography

1	D W Anderson, Universal coefficient theorems for K-theory, preprint (1970)
2	M Ando, M J Hopkins, C Rezk, Multiplicative orientations of KO–theory and of the spectrum of topological modular forms, preprint (2010)
3	S Araki, Orientations in τ–cohomology theories, Japan. J. Math. 5 (1979) 403 MR614829
4	M F Atiyah, K–theory and reality, Quart. J. Math. Oxford Ser. 17 (1966) 367 MR0206940
5	A Baker, B Richter, Invertible modules for commutative 𝕊–algebras with residue fields, Manuscripta Math. 118 (2005) 99 MR2171294
6	T Bauer, Computation of the homotopy of the spectrum tmf, from: "Groups, homotopy and configuration spaces" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13, Geom. Topol. Publ. (2008) 11 MR2508200
7	M Behrens, A modular description of the K(2)–local sphere at the prime 3, Topology 45 (2006) 343 MR2193339
8	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
9	M Behrens, M Hill, M J Hopkins, M Mahowald, On the existence of a v₂³²–self map on M(1,4) at the prime 2, Homology Homotopy Appl. 10 (2008) 45 MR2475617
10	M Behrens, K Ormsby, On the homotopy of Q(3) and Q(5) at the prime 2, Algebr. Geom. Topol. 16 (2016) 2459 MR3572338
11	M Behrens, K Ormsby, N Stapleton, V Stojanoska, On the ring of cooperations for 2–primary connective topological modular forms, preprint (2015) arXiv:1501.01050
12	M Behrens, S Pemmaraju, On the existence of the self map v₂⁹ on the Smith–Toda complex V (1) at the prime 3, 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) 9 MR2066495
13	A J Blumberg, M A Hill, Operadic multiplications in equivariant spectra, norms, and transfers, Adv. Math. 285 (2015) 658 MR3406512
14	U Bunke, T Nikolaus, Twisted differential cohomology, preprint (2014) arXiv:1406.3231
15	K Cesnavicius, A modular description of 𝒳₀(n), preprint (2015) arXiv:1511.07475
16	B Conrad, Arithmetic moduli of generalized elliptic curves, J. Inst. Math. Jussieu 6 (2007) 209 MR2311664
17	P Deligne, M Rapoport, Les schémas de modules de courbes elliptiques, from: "Modular functions of one variable, II", Lecture Notes in Math. 349, Springer (1973) 143 MR0337993
18	D Dugger, Multiplicative structures on homotopy spectral sequences, II, preprint (2003) arXiv:math/0305187
19	A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, 47, Amer. Math. Soc. (1997) MR1417719
20	P G Goerss, Realizing families of Landweber exact homology theories, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16, Geom. Topol. Publ. (2009) 49 MR2544386
21	U Görtz, T Wedhorn, Algebraic geometry, I : Schemes with examples and exercises, Vieweg + Teubner (2010) MR2675155
22	J P C Greenlees, L Meier, Gorenstein duality for Real spectra, preprint (2016) arXiv:1607.02332
23	M Groth, A short course on ∞–categories, preprint (2010) arXiv:1007.2925
24	R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
25	R Hartshorne, Stable reflexive sheaves, Math. Ann. 254 (1980) 121 MR597077
26	M A Hill, The String bordism of BE₈ and BE₈ × BE₈ through dimension 14, Illinois J. Math. 53 (2009) 183 MR2584941
27	M A Hill, The equivariant slice filtration: a primer, Homology Homotopy Appl. 14 (2012) 143 MR3007090
28	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
29	M Hill, T Lawson, Topological modular forms with level structure, Invent. Math. 203 (2016) 359 MR3455154
30	H Hohnhold, The Landweber exact functor theorem, 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) 35 MR3223024
31	M Hovey, J H Palmieri, N P Strickland, Axiomatic stable homotopy theory, 610, Amer. Math. Soc. (1997) MR1388895
32	P Hu, I Kriz, Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence, Topology 40 (2001) 317 MR1808224
33	A Joyal, The theory of quasi-categories and its applications, lecture notes (2008)
34	N M Katz, B Mazur, Arithmetic moduli of elliptic curves, 108, Princeton University Press (1985) MR772569
35	J Konter, The homotopy groups of the spectrum Tmf, preprint (2012) arXiv:1212.3656
36	P S Landweber, Conjugations on complex manifolds and equivariant homotopy of MU, Bull. Amer. Math. Soc. 74 (1968) 271 MR0222890
37	T Lawson, N Naumann, Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2, Int. Math. Res. Not. 2014 (2014) 2773 MR3214285
38	L G Lewis Jr., M A Mandell, Equivariant universal coefficient and Künneth spectral sequences, Proc. London Math. Soc. 92 (2006) 505 MR2205726
39	J Lurie, Higher topos theory, 170, Princeton University Press (2009) MR2522659
40	J Lurie, A survey of elliptic cohomology, from: "Algebraic topology" (editors N A Baas, E M Friedlander, B Jahren, P A Østvær), Abel Symp. 4, Springer (2009) 219 MR2597740
41	J Lurie, Chromatic homotopy theory, lecture notes (2010)
42	J Lurie, Derived algebraic geometry, VIII : Quasi-coherent sheaves and Tannaka duality theorems, unpublished manuscript (2011)
43	J Lurie, Derived algebraic geometry, XII : Proper morphisms, completions, and the Grothendieck existence theorem, unpublished manuscript (2011)
44	J Lurie, Higher algebra, unpublished manuscript (2014)
45	M Mahowald, M Hopkins, The structure of 24 dimensional manifolds having normal bundles which lift to BO[8], from: "Recent progress in homotopy theory" (editors D M Davis, J Morava, G Nishida, W S Wilson, N Yagita), Contemp. Math. 293, Amer. Math. Soc. (2002) 89 MR1887530
46	M Mahowald, C Rezk, Topological modular forms of level 3, Pure Appl. Math. Q. 5 (2009) 853 MR2508904
47	M A Mandell, J P May, Equivariant orthogonal spectra and S–modules, 755, Amer. Math. Soc. (2002) MR1922205
48	M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001) 441 MR1806878
49	A Mathew, The homology of tmf, Homology Homotopy Appl. 18 (2016) 1 MR3515195
50	A Mathew, L Meier, Affineness and chromatic homotopy theory, J. Topol. 8 (2015) 476 MR3356769
51	A Mathew, V Stojanoska, The Picard group of topological modular forms via descent theory, Geom. Topol. 20 (2016) 3133 MR3590352
52	L Meier, United elliptic homology, PhD thesis, University of Bonn (2012)
53	L Meier, Vector bundles on the moduli stack of elliptic curves, J. Algebra 428 (2015) 425 MR3314299
54	N Naumann, The stack of formal groups in stable homotopy theory, Adv. Math. 215 (2007) 569 MR2355600
55	N Naumann, M Spitzweck, P A Østvær, Motivic Landweber exactness, Doc. Math. 14 (2009) 551 MR2565902
56	N Ricka, Equivariant Anderson duality and Mackey functor duality, Glasg. Math. J. 58 (2016) 649 MR3530492
57	J Rognes, Galois extensions of structured ring spectra, Stably dualizable groups, 898, Amer. Math. Soc. (2008) MR2387923
58	S Schwede, Lectures on equivariant stable homotopy theory, lecture notes (2014)
59	M Spitzweck, Operads, algebras and modules in general model categories, preprint (2001) arXiv:math/0101102
60	V Stojanoska, Duality for topological modular forms, Doc. Math. 17 (2012) 271 MR2946825