TY - JOUR
AU - Heard, Drew
PY - 2024/02/26
Y2 - 2024/09/11
TI - Invertible objects in Franke's comodule categories
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 130
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-142361
UR - https://www.mscand.dk/article/view/142361
SP -
AB - <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 $2p-2 > n^2+n$, 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>
ER -