Iwasawa theory for k(1)-local spectra
Iwasawa theory for k(1)-local spectra
复制标题
k(1)-局部谱的 Iwasawa 理论
DOI：
10.1090/s0002-9947-07-04204-3
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发表时间：
2007
影响因子：
1.3
通讯作者：
S. A. Mitchell
中科院分区：
文献类型：
--
作者：
Rebekah Hahn;S. A. Mitchell
岩泽代数是环上的一元幂级数环。长期以来，数论家一直在数域扩张的背景下对它进行研究。然而，它也是作为拓扑论中的一个运算环出现的。本文利用岩泽代数上模的结构理论，研究了-局部稳定同伦理论。特别地，对于奇数，我们将-局部谱分类到伪等价(类似于-模的伪同构)，并给出了弱对偶化谱的厚子范畴的一个岩泽理论分类。
The Iwasawa algebra is a power series ring in one variable over the -adic integers. It has long been studied by number theorists in the context of -extensions of number fields. It also arises, however, as a ring of operations in -adic topological -theory. In this paper we study -local stable homotopy theory using the structure theory of modules over the Iwasawa algebra. In particular, for odd we classify -local spectra up to pseudo-equivalence (the analogue of pseudo-isomorphism for -modules) and give an Iwasawa-theoretic classification of the thick subcategories of the weakly dualizable spectra.