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Milnor Invariants and l-Class Groups

  • Masanori Morishita
Part of the Progress in Mathematics book series (PM, volume 265)

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.

Keywords

Arithmetic topology Milnor invariant class group 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Masanori Morishita
    • 1
  1. 1.Graduate School of MathematicsKyushu UniversityFukuokaJapan

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