Abstract
We consider a nontrivial action of C2 on the type 1 spectrum Y: = M2(1) ^ C(n), which is well-known for admitting a 1-periodic v1-self-map. The resultant finite C2-equivariant spectrum yC2 can also be viewed as the complex points of a finite (Formula presented)-motivic spectrum (Formula presented). In this paper, we show that one of the 1-periodic v1-self-maps of y can be lifted to a self-map of yC2 as well as (Formula presented). Further, the cofiber of the self-map of (Formula presented) is a realization of the subalgebra (Formula presented) (1) of the R-motivic Steenrod algebra. We also show that the C2-equivariant self-map is nilpotent on the geometric fixed-points of yC2.
Original language | English |
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Pages (from-to) | 299-324 |
Number of pages | 26 |
Journal | Homology, Homotopy and Applications |
Volume | 24 |
Issue number | 1 |
DOIs | |
State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022. Prasit Bhattacharya, Bertrand Guillou and Ang Li. All Rights Reserved.
Keywords
- equivariant homotopy
- motivic homotopy
- self-map
ASJC Scopus subject areas
- Mathematics (miscellaneous)