On sheaves in finite group representations

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On sheaves in finite group representations

Xiong, Tengfei; Xu, Fei

Journal of pure and applied algebra, October 2022, 2022-10-00, Volume: 226, Issue: 10

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Given a general finite group G, we consider several categories built on it, their Grothendieck topologies and resulting sheaf categories. For a certain class of transporter categories and their quotients, equipped with atomic topology, we explicitly compute their sheaf categories via sheafification. This enables us to identify G-representations with various fixed-point sheaves. As a consequence, it provides an intrinsic new proof to the equivalence of M. Artin between the category of sheaves on the orbit category and that of group representations.

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