𝐶₂-equivariant and ℝ-motivic stable stems II

Belmont, Eva; Guillou, Bertrand; Isaksen, Daniel

doi:10.1090/proc/15167

-equivariant and $\mathbb{R}$ -motivic stable stems II

Authors: Eva Belmont, Bertrand J. Guillou and Daniel C. Isaksen
Journal: Proc. Amer. Math. Soc. 149 (2021), 53-61
MSC (2010): Primary 14F42, 55Q45, 55Q91, 55T15
DOI: https://doi.org/10.1090/proc/15167
Published electronically: October 16, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the stable homotopy groups of the -equivariant sphere spectrum and the $\mathbb{R}$ -motivic sphere spectrum are isomorphic in a range. This result supersedes previous work of Dugger and the third author.

[1] Eva Belmont and Daniel C. Isaksen, $\mathbb{R}$ -motivic stable stems (2020), preprint.
[2] Daniel Dugger and Daniel C. Isaksen, The motivic Adams spectral sequence, Geom. Topol. 14 (2010), no. 2, 967–1014. MR 2629898, https://doi.org/10.2140/gt.2010.14.967
[3] Daniel Dugger and Daniel C. Isaksen, Low-dimensional Milnor-Witt stems over ℝ, Ann. K-Theory 2 (2017), no. 2, 175–210. MR 3590344, https://doi.org/10.2140/akt.2017.2.175
[4] Daniel Dugger and Daniel C. Isaksen, ℤ/2-equivariant and ℝ-motivic stable stems, Proc. Amer. Math. Soc. 145 (2017), no. 8, 3617–3627. MR 3652813, https://doi.org/10.1090/proc/13505
[5] Bogdan Gheorghe, Guozhen Wang, and Zhouli Xu, The special fiber of the motivic deformation of the stable homotopy category is algebraic, Acta. Math., to appear.
[6] Bertrand J. Guillou, Michael A. Hill, Daniel C. Isaksen, and Douglas Conner Ravenel, The cohomology of 𝐶₂-equivariant \Cal𝐴(1) and the homotopy of 𝑘𝑜_{𝐶₂}, Tunis. J. Math. 2 (2020), no. 3, 567–632. MR 4041284, https://doi.org/10.2140/tunis.2020.2.567
[7] Bertrand J. Guillou and Daniel C. Isaksen, The Bredon-Landweber region in -equivariant stable homotopy groups, preprint, available at arXiv:1907.01539.
[8] J. Heller and K. Ormsby, Galois equivariance and stable motivic homotopy theory, Trans. Amer. Math. Soc. 368 (2016), no. 11, 8047–8077. MR 3546793, https://doi.org/10.1090/S0002-9947-2016-06647-7
[9] Daniel C. Isaksen, Stable stems, Mem. Amer. Math. Soc. 262 (2019), no. 1269, viii+159. MR 4046815, https://doi.org/10.1090/memo/1269
[10] Daniel C. Isaksen, Guozhen Wang, and Zhouli Xu, More stable stems (2020), preprint.
[11] Haynes Robert Miller, SOME ALGEBRAIC ASPECTS OF THE ADAMS-NOVIKOV SPECTRAL SEQUENCE, ProQuest LLC, Ann Arbor, MI, 1975. Thesis (Ph.D.)–Princeton University. MR 2625232
[12] S. P. Novikov, Methods of algebraic topology from the point of view of cobordism theory, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 855–951 (Russian). MR 0221509
[13] Fabien Morel and Vladimir Voevodsky, 𝐴¹-homotopy theory of schemes, Inst. Hautes Études Sci. Publ. Math. 90 (1999), 45–143 (2001). MR 1813224

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14F42, 55Q45, 55Q91, 55T15

Retrieve articles in all journals with MSC (2010): 14F42, 55Q45, 55Q91, 55T15

Additional Information

Eva Belmont
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: ebelmont@northwestern.edu

Bertrand J. Guillou
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: bertguillou@uky.edu

Daniel C. Isaksen
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: isaksen@wayne.edu

DOI: https://doi.org/10.1090/proc/15167
Keywords: Stable homotopy group, equivariant stable homotopy theory, motivic stable homotopy theory, Adams spectral sequence
Received by editor(s): January 29, 2020
Received by editor(s) in revised form: April 27, 2020
Published electronically: October 16, 2020
Additional Notes: The second author was supported by NSF grant DMS-1710379.
The third author was supported by NSF grant DMS-1904241.
Article copyright: © Copyright 2020 American Mathematical Society