Milnor invariants and l-class groups

Masanori Morishita

doi:10.1007/978-3-7643-8608-5_16

Milnor invariants and l-class groups

Masanori Morishita

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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 language	English
Title of host publication	Progress in Mathematics
Publisher	Springer Basel
Pages	669-683
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-7643-8608-5_16
Publication status	Published - Jan 1 2008

Publication series

Name	Progress in Mathematics
Volume	265
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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