连通K理论中的运算

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2023-09-09 DOI:10.2140/ant.2023.17.1595

Alexander Merkurjev, Alexander Vishik

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引用次数: 0

摘要

我们对具有不同无扭系数的连通K理论中的加法运算进行了分类。我们发现，积分情况的答案需要理解ℤ^ 案例此外，尽管积分加法运算在拓扑上是由亚当斯运算生成的，但这些运算并没有被简化为后者的无限线性组合。我们描述了稳定运算的拓扑基，并将其与分级K理论中稳定运算的一个基联系起来。我们在这两个理论中对乘法运算进行了分类，并证明了具有ℤ^-系数是由稳定的乘法运算拓扑生成的。对于积分运算，情况并非如此。

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Operations in connective K-theory

We classify additive operations in connective K-theory with various torsion-free coefficients. We discover that the answer for the integral case requires understanding of the $\hat{ℤ}$ case. Moreover, although integral additive operations are topologically generated by Adams operations, these are not reduced to infinite linear combinations of the latter ones. We describe a topological basis for stable operations and relate it to a basis of stable operations in graded K-theory. We classify multiplicative operations in both theories and show that homogeneous additive stable operations with $\hat{ℤ}$ -coefficients are topologically generated by stable multiplicative operations. This is not true for integral operations.

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.