@article{Heard_2024, title={Invertible objects in Franke’s comodule categories}, volume={130}, url={https://www.mscand.dk/article/view/142361}, DOI={10.7146/math.scand.a-142361}, abstractNote={<p>We study the Picard group of Franke’s category of quasi-periodic $E_0E$-comodules for $E$ a 2-periodic Landweber exact cohomology theory of height $n$ such as Morava $E$-theory, showing that for $2p-2 &gt; n^2+n$, this group is infinite cyclic, generated by the suspension of the unit. This is analogous to, but independent of, the corresponding calculations by Hovey and Sadofsky in the $E$-local stable homotopy category. We also give a computation of the Picard group of $I_n$-complete quasi-periodic $E_0E$-comodules when $E$ is Morava $E$-theory, as studied by Barthel-Schlank-Stapleton for $2p-2 \ge n^2$ and $p-1
mid n$, and compare this to the Picard group of the $K(n)$-local stable homotopy category, showing that they agree up to extension.</p>}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Heard, Drew}, year={2024}, month={Feb.} }