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Local systems with restricted variation on the formal punctured disc via factorization

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arxiv 2411.05297 v1 pith:AFTDHNSK submitted 2024-11-08 math.AG math.RT

classification math.AGmath.RT
keywords factorizationcategoriesdiscformallocalrestrictedstacksystems
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We define the stack of $G$-local systems with restricted variation on the formal puntured disc and study its properties. We embed sheaves of categories over this stack into the category of factorization module categories over $\operatorname{Rep}(G)$. Along the way we develop a theory of factorization structures in families and study functorialities of such under changes of the base curve.

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Cited by 1 Pith paper

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  1. Iwahori Fundamental Local Equivalence

    math.AG 2026-08 conditional novelty 6.0 of 10

    The author establishes three equivalences of factorization module categories: the Iwahori-ramified versions of the Arkhipov-Bezrukavnikov, Bezrukavnikov, and Fundamental Local Equivalences.

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