Big symplectic or orthogonal monodromy modulo $\ell$

By Chris Hall. 2006

68 citations recorded by the source corpus.

Let k be a field not of characteristic two and L be a set of almost all rational primes invertible in k. Suppose we have a variety X/k and strictly compatible system {M_ell -> X : ell in L} of constructible F_ell-sheaves. If the system is orthogonally or symplectically self-dual, then the geometric monodromy group of M_ell is a subgroup of a corresponding isometry group G_ell over F_ell, and we say it has big monodromy if it contains the derived subgroup DG_ell=[G_ell,G_ell]. We prove a theorem which gives sufficient conditions for M_ell 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 ell and the system.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/9b282bc5f9a6f501a11326b0229cfd54a305a41c

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In Discrete Mathematics and Combinatorics

1. R. Pries
2. Jeff Achter

In Geometry and Topology

1. R. Pries
2. Jeff Achter
3. Chris Hall

In Information Systems

1. R. Pries
2. Jeff Achter

Citations in the corpus

• The integral monodromy of hyperelliptic and trielliptic curves (2006, background): “While this article was in review, C. Hall posted another proof of Theorem 3.4 along with a generalization to elliptic surfaces [ 14 ].”