Picard Groups of the Stable Module Category for Quaternion Groups

Richard Wong (University of Texas at Austin)

Resumen: One problem of interest in modular representation theory of finite groups is in computing the group of endo-trivial modules. In homotopy theory, this group is known as the Picard group of the stable module category. This group was originally computed by Carlson-Thévenaz using the theory of support varieties. However, jointly with Jeroen van der Meer, we provide new, homotopical proofs of their results for the quaternion group of order 8, generalized quaternion groups, and cyclic p-groups using descent methods.