collaborators

6 papers

math.GR2026

The fusion-stable tom Dieck homomorphism

Sam K. Miller

Tornehave and Yalçin proved that the tom Dieck homomorphism, which sends a virtual real representation to a unit of the Burnside ring, is surjective for any -group . We prove…

math.RT2026

The classification of integral endotrivial complexes

Juan Omar Gómez, Sam K. Miller

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 r…

math.RT2026

On endosplit -permutation resolutions and Broué's conjecture for -solvable groups

Sam K. Miller

Endosplit -permutation resolutions play an instrumental role in verifying Broué's abelian defect group conjecture in numerous cases. We give a new characterization of all endos…

math.RT2025

The Euler characteristic of an endotrivial complex

Nadia Mazza, Sam K. Miller

Let be a finite group and a field of prime characteristic . We examine the Lefschetz homomorphism from the group of endotrivial compl…

math.GR2025

The classification of endotrivial complexes

Sam K. Miller

Let be a finite group and a field of prime characteristic . We give a complete classification of endotrivial complexes, i.e. determine the Picard group $\mathcal{E}_k(G)…

math.GR2025

Relatively endotrivial complexes

Sam K. Miller

Let be a finite group and be a field of characteristic . In prior work, we studied endotrivial complexes, the invertible objects of the bounded homotopy category $K^…