Geometry & Topology Volume 30, issue 5 (2026)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Galois reconstruction of Artin–Tate $\mathbb{R}$-motivic spectra

Robert Burklund, Jeremy Hahn and Andrew Senger

Geometry & Topology 30 (2026) 1625–1717

DOI: 10.2140/gt.2026.30.1625

Bibliography

1	J F Adams, Stable homotopy and generalised homology (editor I Kaplansky), University of Chicago Press (1974) MR1324104
2	T Bachmann, Motivic and real étale stable homotopy theory, Compos. Math. 154 (2018) 883 MR3781990
3	T Bachmann, Rigidity in étale motivic stable homotopy theory, Algebr. Geom. Topol. 21 (2021) 173 MR4224739
4	T Bachmann, M J Hopkins, η-periodic motivic stable homotopy theory over fields, (2020) arXiv:2005.06778
5	T Bachmann, M Hoyois, Norms in motivic homotopy theory, 425, Soc. Math. France (2021) MR4288071
6	T Bachmann, E Elmanto, P A Østvær, Stable motivic invariants are eventually étale local, (2020) arXiv:2003.04006v2
7	T Bachmann, H J Kong, G Wang, Z Xu, The Chow t-structure on the ∞-category of motivic spectra, Ann. of Math. (2) 195 (2022) 707 MR4387236
8	T Barthel, D Heard, G Valenzuela, Local duality in algebra and topology, Adv. Math. 335 (2018) 563 MR3836674
9	M Behrens, J Shah, C₂-equivariant stable homotopy from real motivic stable homotopy, Ann. K-Theory 5 (2020) 411 MR4132743
10	E Belmont, B J Guillou, D C Isaksen, C₂-equivariant and ℝ-motivic stable stems, II, Proc. Amer. Math. Soc. 149 (2021) 53 MR4172585
11	M V Bondarko, Weight structures vs. t-structures ; weight filtrations, spectral sequences, and complexes (for motives and in general), J. K-Theory 6 (2010) 387 MR2746283
12	R Burklund, An extension in the Adams spectral sequence in dimension 54, Bull. Lond. Math. Soc. 53 (2021) 404 MR4239183
13	R Burklund, J Hahn, A Senger, On the boundaries of highly connected, almost closed manifolds, Acta Math. 231 (2023) 205 MR4683371
14	D Dugger, D C Isaksen, Motivic cell structures, Algebr. Geom. Topol. 5 (2005) 615 MR2153114
15	D Dugger, D C Isaksen, The motivic Adams spectral sequence, Geom. Topol. 14 (2010) 967 MR2629898
16	E Elmanto, J Shah, Scheiderer motives and equivariant higher topos theory, Adv. Math. 382 (2021) 107651 MR4224049
17	B Gheorghe, The motivic cofiber of τ, Doc. Math. 23 (2018) 1077 MR3874951
18	B Gheorghe, D C Isaksen, The structure of motivic homotopy groups, Bol. Soc. Mat. Mex. (3) 23 (2017) 389 MR3633139
19	B Gheorghe, G Wang, Z Xu, The special fiber of the motivic deformation of the stable homotopy category is algebraic, Acta Math. 226 (2021) 319 MR4281382
20	B Gheorghe, D C Isaksen, A Krause, N Ricka, ℂ-motivic modular forms, J. Eur. Math. Soc. 24 (2022) 3597 MR4432907
21	P G Goerss, Quasi-coherent sheaves on the moduli stack of formal groups, (2008) arXiv:0802.0996
22	T Gregersen, A Singer construction in motivic homotopy theory, PhD thesis, University of Oslo (2012)
23	B J Guillou, M A Hill, D C Isaksen, D C Ravenel, The cohomology of C₂-equivariant 𝒜(1) and the homotopy of ko_C₂, Tunis. J. Math. 2 (2020) 567 MR4041284
24	D Heard, On equivariant and motivic slices, Algebr. Geom. Topol. 19 (2019) 3641 MR4045363
25	J Heller, K Ormsby, Galois equivariance and stable motivic homotopy theory, Trans. Amer. Math. Soc. 368 (2016) 8047 MR3546793
26	J Heller, K Ormsby, The stable Galois correspondence for real closed fields, from: "New directions in homotopy theory" (editors N Kitchloo, M Merling, J Morava, E Riehl, W S Wilson), Contemp. Math. 707, Amer. Math. Soc. (2018) 1 MR3807738
27	M A Hill, M J Hopkins, D C Ravenel, On the nonexistence of elements of Kervaire invariant one, Ann. of Math. (2) 184 (2016) 1 MR3505179
28	M Hoyois, From algebraic cobordism to motivic cohomology, J. Reine Angew. Math. 702 (2015) 173 MR3341470
29	M Hoyois, The six operations in equivariant motivic homotopy theory, Adv. Math. 305 (2017) 197 MR3570135
30	M Hoyois, S Kelly, P A Østvær, The motivic Steenrod algebra in positive characteristic, J. Eur. Math. Soc. 19 (2017) 3813 MR3730515
31	P Hu, On the Picard group of the stable 𝔸¹-homotopy category, Topology 44 (2005) 609 MR2122218
32	P Hu, I Kriz, Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence, Topology 40 (2001) 317 MR1808224
33	P Hu, I Kriz, K Ormsby, Convergence of the motivic Adams spectral sequence, J. K-Theory 7 (2011) 573 MR2811716
34	P Hu, I Kriz, K Ormsby, Remarks on motivic homotopy theory over algebraically closed fields, J. K-Theory 7 (2011) 55 MR2774158
35	D C Isaksen, Stable stems, 1269, Amer. Math. Soc. (2019) MR4046815
36	H J Kong, The C₂-effective spectral sequence for C₂-equivariant connective real K-theory, (2020) arXiv:2004.00806
37	P S Landweber, Fixed point free conjugations on complex manifolds, Ann. of Math. (2) 86 (1967) 491 MR220317
38	P S Landweber, Conjugations on complex manifolds and equivariant homotopy of MU, Bull. Amer. Math. Soc. 74 (1968) 271 MR222890
39	M Levine, A comparison of motivic and classical stable homotopy theories, J. Topol. 7 (2014) 327 MR3217623
40	M Levine, The Adams–Novikov spectral sequence and Voevodsky’s slice tower, Geom. Topol. 19 (2015) 2691 MR3416112
41	W H Lin, On conjectures of Mahowald, Segal and Sullivan, Math. Proc. Cambridge Philos. Soc. 87 (1980) 449 MR556925
42	K Loyd, Box product of C_p-Mackey functors, (2017) arXiv:1710.08560
43	J Lurie, Rotation invariance in algebraic K-theory, preprint (2015)
44	J Lurie, Higher algebra, book draft (2017)
45	J Lurie, Elliptic cohomology, II : Orientations, preprint (2018)
46	J Lurie, Spectral algebraic geometry, book draft (2018)
47	A Mathew, N Naumann, J Noel, Nilpotence and descent in equivariant stable homotopy theory, Adv. Math. 305 (2017) 994 MR3570153
48	F Morel, The stable 𝔸¹-connectivity theorems, K-Theory 35 (2005) 1 MR2240215
49	F Morel, 𝔸¹-algebraic topology, from: "Proceedings of the International Congress of Mathematicians, II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 1035 MR2275634
50	F Morel, V Voevodsky, A¹-homotopy theory of schemes, Inst. Hautes Études Sci. Publ. Math. (1999) 45 MR1813224
51	I Patchkoria, B Sanders, C Wimmer, The spectrum of derived Mackey functors, Trans. Amer. Math. Soc. 375 (2022) 4057 MR4419053
52	P Pelaez, On the functoriality of the slice filtration, J. K-Theory 11 (2013) 55 MR3034283
53	L Positselski, Mixed Artin–Tate motives with finite coefficients, Mosc. Math. J. 11 (2011) 317, 407 MR2859239
54	L Positselski, Galois cohomology of a number field is Koszul, J. Number Theory 145 (2014) 126 MR3253297
55	P Pstrągowski, Synthetic spectra and the cellular motivic category, Invent. Math. 232 (2023) 553 MR4574661
56	M Spitzweck, Relations between slices and quotients of the algebraic cobordism spectrum, Homology Homotopy Appl. 12 (2010) 335 MR2771593
57	R W Thomason, Algebraic K-theory and étale cohomology, Ann. Sci. École Norm. Sup. (4) 18 (1985) 437 MR826102
58	V Voevodsky, Open problems in the motivic stable homotopy theory, I, from: "Motives, polylogarithms and Hodge theory, I" (editors F Bogomolov, L Katzarkov), Int. Press Lect. Ser. 3, Int. (2002) 3 MR1977582
59	V Voevodsky, Motivic cohomology with Z∕2-coefficients, Publ. Math. Inst. Hautes Études Sci. (2003) 59 MR2031199
60	V Voevodsky, Reduced power operations in motivic cohomology, Publ. Math. Inst. Hautes Études Sci. (2003) 1 MR2031198
61	V Voevodsky, Motivic Eilenberg–Mac Lane spaces, Publ. Math. Inst. Hautes Études Sci. (2010) 1 MR2737977
62	M Wendt, More examples of motivic cell structures, (2010) arXiv:1012.0454