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Junior Geometry
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Richard Wong, Zoom: Picard Groups of Stable Module Categories for Quaternion Groups
Tuesday, September 22, 2020, 03:45pm - 04:45pm
One problem of interest in modular representation theory 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 $\StMod(kG)$. This group was computed by work of Carlson-Thevenaz, using group cohomology and the theory of support varieties of modules. Recently, work of Mathew and Mathew-Stojanoska introduced a new, homotopical approach to this computation through faithful Galois descent. While Galois descent often holds in $\StMod(kG)$, it is too much to expect faithful Galois descent. Nevertheless, I show that one can extend their methods to the non-faithful setting in the case that $G$ is a quaternion or generalized quaternion group. This is a practice research talk.
Location: Zoom

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