Higher Chern classes in Iwasawa theory
Higher Chern classes in Iwasawa theory
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DOI：
10.1353/ajm.2020.0017
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发表时间：
2015-12
影响因子：
1.7
通讯作者：
F. Bleher;T. Chinburg;Richard Greenberg;M. Kakde;G. Pappas;R. Sharifi;M. Taylor
中科院分区：
文献类型：
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作者：
F. Bleher;T. Chinburg;Richard Greenberg;M. Kakde;G. Pappas;R. Sharifi;M. Taylor
摘要：我们开始研究 Iwasawa 模块的 $m$th Chern 类和 $m$th 特征符号，这些模块的余维至少支持 $m$。这扩展了特征理想的经典理论及其对于岩泽模块的生成器，岩泽模块是扭转的，即在余维中支持至少 1 美元。我们将其应用于由虚二次域的阿贝尔扩张的理想类群的 $p$ 部分的逆极限构造的 Iwasawa 模块。当这个模块是伪空时（推测总是如此），我们确定它的第二个 Chern 类，并表明它具有由两个 Katz $p$-adic $L$-函数的 Steinberg 符号给出的特征符号。
abstract:We begin a study of $m$th Chern classes and $m$th characteristic symbols for Iwasawa modules which are supported in codimension at least $m$. This extends the classical theory of characteristic ideals and their generators for Iwasawa modules which are torsion, i.e., supported in codimension at least $1$. We apply this to an Iwasawa module constructed from an inverse limit of $p$-parts of ideal class groups of abelian extensions of an imaginary quadratic field. When this module is pseudo-null, which is conjecturally always the case, we determine its second Chern class and show that it has a characteristic symbol given by the Steinberg symbol of two Katz $p$-adic $L$-functions.