Sam K. Miller

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20242026

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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.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 $Λ : E_{k} (G) \to O (T (k G))$ from the group of endotrivial comple…

math.RT2024

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

Sam K. Miller

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

math.RT2023

Endotrivial complexes

Sam K. Miller

Let $G$ be a finite group, $p$ a prime, and $k$ a field of characteristic $p$ . We introduce the notion of an endotrivial chain complex of $p$ -permutation $k G$ -modules, which are th…

The classification of integral endotrivial complexes

The Euler characteristic of an endotrivial complex

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

Endotrivial complexes

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