Big symplectic or orthogonal monodromy modulo $\ell$
Big symplectic or orthogonal monodromy modulo $\ell$
复制标题
大辛或正交单向模$ell$
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Chris Hall
中科院分区：
文献类型：
--
作者：
Chris Hall
设k是一个不具有特征二的域，L是k中可逆的几乎所有有理数的集合。假设我们有一个可构造f_ell -束的变种X/k和严格相容系统{M_ell -> X: ell in L}。如果系统是正交自对偶或对称自对偶的，则M_ell的几何单群是F_ell上对应的等距群G_ell的子群，如果它包含派生的子群DG_ell=[G_ell,G_ell]，我们说它有大单群。我们证明了一个定理，给出了M_ell具有大单态的充分条件。我们将该定理应用于由超椭圆曲线和椭圆曲面族的中上同调引起的显式系统，证明了随着系统的变化，系统的单调性是一致大的。
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.