Milnor invariants and l-class groups

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    Following the analogies between knots and primes, we introduce arithmetic analogues of higher linking matrices for prime numbers by using the arithmetic Milnor numbers. As an application, we describe the Galois module structure of the l-class group of a cyclic extension of ℚ of degree l (l being a prime number) in terms of the arithmetic higher linking matrices. In particular, our formula generalizes the classical formula of Rédei on the 4 and 8 ranks of the 2-class group of a quadratic field.

    Original languageEnglish
    Title of host publicationProgress in Mathematics
    PublisherSpringer Basel
    Pages669-683
    Number of pages15
    DOIs
    Publication statusPublished - 2008

    Publication series

    NameProgress in Mathematics
    Volume265
    ISSN (Print)0743-1643
    ISSN (Electronic)2296-505X

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Algebra and Number Theory
    • Geometry and Topology

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