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• W3033506490 abstract "We introduce a notion of volume for an l-adic local system over an algebraic curve and, under some conditions, give a symplectic form on the rigid analytic deformation space of the corresponding geometric local system. These constructions can be viewed as arithmetic analogues of the volume and the Chern-Simons invariants of a representation of the fundamental group of a 3-manifold which fibers over the circle and of the symplectic form on the character varieties of a Riemann surface. We show that the absolute Galois group acts on the deformation space by conformal symplectomorphisms which extend to an l-adic analytic flow. We also prove that the locus of the deformation space over which the local system suitably descends is the critical set of a collection of rigid analytic functions. The vanishing cycles of these functions give additional invariants." @default.
• W3033506490 created "2020-06-12" @default.
• W3033506490 creator A5029243115 @default.
• W3033506490 date "2020-06-05" @default.
• W3033506490 modified "2023-09-25" @default.
• W3033506490 title "Volume and symplectic structure for l-adic local systems" @default.
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• W3033506490 doi "https://doi.org/10.48550/arxiv.2006.03668" @default.
• W3033506490 hasPublicationYear "2020" @default.
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