Abstract:We describe the group of endotrivial complexes, i.e., the Picard group, of the derived category of permutation modules for a finite group over a commutative Noetherian ring. As a result, we deduce that not every endotrivial with integer coefficients arises from a homotopy representation, i.e., an invertible genuine equivariant spectrum. Along the way, we establish a descent result with respect to subgroups of prime-power order, show that oriented endotrivial complexes are line bundles, that is, locally trivial with respect to an open cover of the Balmer spectrum, and provide a topological construction of forerunner homomorphisms, answering a question of the second-named author.
From: Sam Miller [view email]
[v1]
Fri, 29 May 2026 10:40:12 UTC (60 KB)
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