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arXiv · 2603.22171

The exceptional locus of a motivic local system

Luca Terenzi
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Abstract

To every Nori motivic local system over a smooth, connected complex algebraic variety, we associate an exceptional locus controlling the variation in the complexity of its stalks; the definition is given explicitly in terms of motivic Galois groups and Artin motives. We prove a motivic analogue of the Cattani--Deligne--Kaplan Theorem, asserting that the exceptional locus is a countable union of closed algebraic subvarieties. Moreover, we show that it is defined over any algebraically closed subfield over which the motivic local system admits a model, and stable under Galois conjugation when the latter descends to a smaller subfield. This extends and strengthens previous results by Andr\'e in the pure case. We obtain a similar description for the splitting locus of the motivic weight filtration.

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Luca Terenzi. 2026-03-23. The exceptional locus of a motivic local system. https://arxiv.org/abs/2603.22171

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