Sam K. Miller

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math.RT2026

The classification of integral endotrivial complexes

Juan Omar GÃ³mez, 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 $p$ -permutation resolutions and BrouÃ©'s conjecture for $p$ -solvable groups

Sam K. Miller

Endosplit $p$ -permutation resolutions play an instrumental role in verifying BrouÃ©'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 $G$ be a finite group and $k$ a field of prime characteristic $p$ . We examine the Lefschetz homomorphism $I^ : E_{k} (G) \to O (T (k G))$ from the group of endotrivial compl…

The classification of integral endotrivial complexes

On endosplit p-permutation resolutions and BrouÃ©'s conjecture for p-solvable groups

The Euler characteristic of an endotrivial complex

On endosplit $p$ -permutation resolutions and BrouÃ©'s conjecture for $p$ -solvable groups