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This is a Quantitative Study study.

September 29, 2025Open Access

The spectrum of local dualisable modular representations

Key Points

The spectrum is calculated for local dualisable modular representations in group algebra contexts.
Focused on $ au$-local and $ au$-torsion objects, assessing their implications in finite groups.
This approach enhances understanding of modular representations through tensor triangulated categories.
The findings contribute to the exploration of stable module categories over group algebras.

Abstract

For a point p in the spectrum of the cohomology ring of a finite group G over a field k, we calculate the spectrum for the subcategory of dualisable objects inside the tensor triangulated category of p-local and p-torsion objects in the (big) stable module category of the group algebra kG.

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Cite This Study

Benson et al. (Sun,) studied this question.

synapsesocial.com/papers/68da58e0c1728099cfd11911 https://doi.org/https://doi.org/10.48550/arxiv.2505.19368

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