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

2023/06/21 by Gao Xu, Ang Li, Gao, Xu +1
Mathematics · Biochemistry, Genetics and Molecular Biology · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.2306.12527

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 ℝ-motivic mod 2 Steenrod subalgebra A(1)^ℝ. Our computation shows that Pic(A(1)^ℝ) is isomorphic to ℤ⁴, where two ranks come from the motivic grading, one from the algebraic loop functor, and the last is generated by the ℝ-motivic joker J.

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