论文标题
表面和应用的平面捆绑包的共同体界限
Cohomological boundedness for flat bundles on surfaces and applications
论文作者
论文摘要
本文探讨了模量空间存在于无限范围和不规则性的扁平束空间的共同体学后果，并提供了无条件的证据。也就是说，我们证明了存在的普遍界限，这是de rham同提的维度的扁平捆绑包和表面上有界限和不规则性的维度。在任何维度上，我们都证明了lefschetz识别原理，表明在限制后具有有界等级和不规则性的平面束的存在。我们在任何维度上获得了具有有界等级和不规则性的扁平束位基因座的程度的通用界限。一路走来，我们在光滑的表面（部分差异）上对B型分散器组引入了新操作，并证明了表面上扁平捆绑包的特征周期的封闭公式，这是根据Kedlaya与任何Flate Bucledle by buctive bucts buctiale buctecte bucts buctecte buctecte bucte的局部差异的部分差异。
This paper explores the cohomological consequences of the existence of moduli spaces for flat bundles with bounded rank and irregularity at infinity and gives unconditional proofs. Namely, we prove the existence of a universal bound for the dimension of De Rham cohomology of flat bundles with bounded rank and irregularity on surfaces. In any dimension, we prove a Lefschetz recognition principle stating the existence of hyperplane sections distinguishing flat bundles with bounded rank and irregularity after restriction. We obtain in any dimension a universal bound for the degrees of the turning loci of flat bundles with bounded rank and irregularity. Along the way, we introduce a new operation on the group of b-divisors on a smooth surface (the partial discrepancy) and prove a closed formula for the characteristic cycles of flat bundles on surfaces in terms of the partial discrepancy of the irregularity b-divisor attached to any flat bundle by Kedlaya.
