论文标题
L-ADIC局部系统的体积和符号结构
Volume and symplectic structure for l-adic local systems
论文作者
论文摘要
我们在代数曲线上引入了L-ADIC局部系统的体积概念，在某些条件下，在相应几何局部系统的刚性分析变形空间上给出了符号形式。这些结构可以看作是体积的算术类似物，而Chern-simons则是3个manifold的基本组的代表，这些构造在圆圈和riemann表面的特征品种上纤维上纤维和符号形式的形式。我们表明，绝对GALOIS组通过延伸至L-ADIC分析流程的形态形态形态作用于变形空间。我们还证明，局部系统适当下降的变形空间的座位是刚性分析功能集合的关键集。这些功能的消失循环产生了其他不变性。
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.
