New York Journal of Mathematics
Volume 26 (2020), 1355-1374


Ang Li

The v1-periodic region in the cohomology of the C-motivic Steenrod algebra

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Published: November 15, 2020.
Keywords: Motivic homotopy theory, Adams spectral sequence, motivic Steenrod algebra.
Subject: 55S30, 55S10, 55T15, 14F42.

We establish a v1-periodicity theorem in Ext over the C-motivic Steenrod algebra. The element h1 of Ext, which detects the homotopy class η in the motivic Adams spectral sequence, is non-nilpotent and therefore generates h1-towers. Our result is that, apart from these h1-towers, v1-periodicity operators give isomorphisms in a range near the top of the Adams chart. This result generalizes well-known classical behavior.


The author would like to thank Bertrand Guillou for useful instructions and helpful discussions. The author also benefited from discussions with J.D. Quigley, Eva Belmont, and Prasit Bhattacharya and appreciates their assistance. The author thanks the referee for providing detailed comments that helped to improve the exposition of the article.

Author information

Ang Li:
Department of Mathematics
The University of Kentucky
Lexington, KY 40506-0027, USA