The stable Picard group of finite Adams Hopf algebroids with an application to the R-motivic Steenrod subalgebra AR(1)

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.