The stable Picard group of finite Adams Hopf algebroids with an application to the [formula omitted]-motivic Steenrod subalgebra [formula omitted]

Abstract

In this paper, we investigate the rigidity of the stable comodule category of a specific class of Hopf algebroids known as finite Adams, shedding light on its Picard group. Then, we establish a reduction process through base changes, enabling us to effectively compute the Picard group of the ▪-motivic mod 2 Steenrod subalgebra▪. Our computation shows that ▪ is isomorphic to ▪, where two ranks come from the motivic grading, one from the algebraic loop functor, and the last is generated by the ▪-motivic joker J.