On Admissible Rank One Local Systems
نویسنده
چکیده
A rank one local system L on a smooth complex algebraic variety M is 1-admissible if the dimension of the first cohomology group H(M,L) can be computed from the cohomology algebra H∗(M, C) in degrees ≤ 2. Under the assumption that M is 1-formal, we show that all local systems, except finitely many, on a non-translated irreducible component W of the first characteristic variety V1(M) are 1-admissible, see Proposition 3.1. The same result holds for local systems on a translated component W , but now H∗(M, C) should be replaced by H∗(M0, C), where M0 is a Zariski open subset obtained from M by deleting some hypersurfaces determined by the translated component W , see Theorem 4.3.
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