15 January 2008 Big symplectic or orthogonal monodromy modulo
Chris Hall
Author Affiliations +
Duke Math. J. 141(1): 179-203 (15 January 2008). DOI: 10.1215/S0012-7094-08-14115-8


Let k be a field not of characteristic two, and let Λ be a set consisting of almost all rational primes invertible in k. Suppose that we have a variety X/k and strictly compatible system {MX:Λ} of constructible F-sheaves. If the system is orthogonally or symplectically self-dual, then the geometric monodromy group of M is a subgroup of a corresponding isometry group Γ over F, and we say that it has big monodromy if it contains the derived subgroup DΓ. We prove a theorem that gives sufficient conditions for M to have big monodromy. We apply the theorem to explicit systems arising from the middle cohomology of families of hyperelliptic curves and elliptic surfaces to show that the monodromy is uniformly big as we vary and the system. We also show how it leads to new results for the inverse Galois problem


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Chris Hall. "Big symplectic or orthogonal monodromy modulo ." Duke Math. J. 141 (1) 179 - 203, 15 January 2008. https://doi.org/10.1215/S0012-7094-08-14115-8


Published: 15 January 2008
First available in Project Euclid: 4 December 2007

zbMATH: 1205.11062
MathSciNet: MR2372151
Digital Object Identifier: 10.1215/S0012-7094-08-14115-8

Primary: 11G05 , 11G10 , 12F12
Secondary: 14D05 , 14H40 , 14J27

Rights: Copyright © 2008 Duke University Press


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Vol.141 • No. 1 • 15 January 2008
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