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 - Jan 1 2008

Publication series

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

Fingerprint

Class Group
Prime number
Linking
Invariant
Galois Module Structure
Milnor number
Quadratic field
Knot
Analogy
Analogue
Generalise

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Morishita, M. (2008). Milnor invariants and l-class groups. In Progress in Mathematics (pp. 669-683). (Progress in Mathematics; Vol. 265). Springer Basel. https://doi.org/10.1007/978-3-7643-8608-5_16

Milnor invariants and l-class groups. / Morishita, Masanori.

Progress in Mathematics. Springer Basel, 2008. p. 669-683 (Progress in Mathematics; Vol. 265).

Research output: Chapter in Book/Report/Conference proceedingChapter

Morishita, M 2008, Milnor invariants and l-class groups. in Progress in Mathematics. Progress in Mathematics, vol. 265, Springer Basel, pp. 669-683. https://doi.org/10.1007/978-3-7643-8608-5_16
Morishita M. Milnor invariants and l-class groups. In Progress in Mathematics. Springer Basel. 2008. p. 669-683. (Progress in Mathematics). https://doi.org/10.1007/978-3-7643-8608-5_16
Morishita, Masanori. / Milnor invariants and l-class groups. Progress in Mathematics. Springer Basel, 2008. pp. 669-683 (Progress in Mathematics).
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