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We explore the relation between cohomology jump loci in a finite Galoiscover, formality properties and algebraic monodromy action. We show that thejump loci of the base and total space are essentially the same, provided thebase space is 1-formal and the monodromy action in degree 1 is trivial. We usereduced multinet structures on line arrangements to construct components of thefirst characteristic variety of the Milnor fiber in degree 1, and to prove thatthe monodromy action is non-trivial in degree 1. For an arbitrary linearrangement, we prove that the triviality of the monodromy in degree 1 can bedetected in a precise way, by resonance varieties.

Finite Galois covers, cohomology jump loci, formality properties, and multinets