Algebraic K-theory of topological K-theory
Algebraic K-theory of topological K-theory
复制标题
拓扑 K 理论的代数 K 理论
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Rognes
中科院分区：
文献类型：
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作者：
Christian Ausoni;J. Rognes
我们对环谱的算术感兴趣。为了理解这一点，我们必须使用结构化环谱，例如 S 代数 [EKMM]、对称环谱 [HSS] 或 Γ 环 [Ly]。我们将这些称为 Salgebras。那么交换对象就是交换 S 代数。环的范畴通过 Eilenberg-MacLane 函子 R →HR 嵌入到 S 代数的范畴中。因此，我们可以将 S 代数视为代数意义上的环的推广。 S-代数增加的灵活性为新的例子和构造提供了空间，这最终也可能揭示环本身的类别。在代数数论中，数域中整数环的算术主要由皮卡德群、单位群和布劳尔群来捕获。这些都是
We are interested in the arithmetic of ring spectra. To make sense of this we must work with structured ring spectra, such as S-algebras [EKMM], symmetric ring spectra [HSS] or Γ-rings [Ly]. We will refer to these as Salgebras. The commutative objects are then commutative S-algebras. The category of rings is embedded in the category of S-algebras by the Eilenberg– MacLane functor R →HR. We may therefore view an S-algebra as a generalization of a ring in the algebraic sense. The added flexibility of S-algebras provides room for new examples and constructions, which may eventually also shed light upon the category of rings itself. In algebraic number theory the arithmetic of the ring of integers in a number field is largely captured by its Picard group, its unit group and its Brauer group. These are