Tate blueshift and vanishing for Real oriented cohomology theories

Li, Guchuan; Lorman, Vitaly; Quigley, J.D.

doi:10.1016/j.aim.2022.108780

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…with domain the spectrum of Real bordism; see Araki and Murayama [2] and Hu and Kriz [22]. These orientations have proved invaluable to the study of 2-local chromatic homotopy theory, leading to an explosion of progress surrounding the Hill-Hopkins-Ravenel solution of the Kervaire invariant one problem; see Beaudry, Bobkova, Hill and Stojanoska [3], Beaudry, Hill, Shi and Zeng [4], Greenlees and Meier [8], Hahn and Shi [9], Heard, Li and Shi [10], Hill and Meier [19], Hill, Hopkins and Ravenel [17], Hill, Shi, Wang and Xu [20], Kitchloo, Lorman and Wilson [23], Li, Lorman and Quigley [25], Li, Shi, Wang and Xu [26] and Meier, Shi and Zeng [28].…”

Section: Introductionmentioning

confidence: 99%

Odd primary analogs of real orientations

2023

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We define, in C p -equivariant homotopy theory for p > 2, a notion of p -orientation analogous to a C 2 -equivariant Real orientation. The definition hinges on a C p -space CP 1p , which we prove to be homologically even, in a sense generalizing recent C 2 -equivariant work on conjugation spaces.We prove that the height p 1 Morava E-theory is p -oriented and that tmf.2/ is 3 -oriented. We explain how a single equivariant map v p 1 W S 2 ! † 1 CP 1 p completely generates the homotopy of E p 1 and tmf.2/, expressing a height-shifting phenomenon pervasive in equivariant chromatic homotopy theory.

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