论文标题
广义的Bockstein地图和Massey产品
Generalized Bockstein maps and Massey products
论文作者
论文摘要
给定一个封闭的正常亚组N的有限P-合子学维度的G组和G的Pro-P商H，我们通过HGEBRA组中的增强理想的能力研究了N的iWasawa iWasawa共同体。对于某些组H，我们将这些广义Bockstein地图的值与Massey产品相对于限制性的定义系统的限制性将其关联起来。我们使用研究来证明某些非亚伯式扩展的p-ranks of the Rational数字的p级别，并提供了Triple Massey Products在Galois Cohom学中消失的新证明。
Given a profinite group G of finite p-cohomological dimension and a pro-p quotient H of G by a closed normal subgroup N, we study the filtration on the Iwasawa cohomology of N by powers of the augmentation ideal in the group algebra of H. We show that the graded pieces are related to the cohomology of G via analogues of Bockstein maps for the powers of the augmentation ideal. For certain groups H, we relate the values of these generalized Bockstein maps to Massey products relative to a restricted class of defining systems depending on H. We apply our study to prove lower bounds on the p-ranks of class groups of certain nonabelian extensions of the rational numbers and to give a new proof of the vanishing of triple Massey products in Galois cohomology.
