@inbook{f933c8fa45854678bd7f7ee62c160cfa,

title = "Milnor invariants and l-class groups",

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 R{\'e}dei on the 4 and 8 ranks of the 2-class group of a quadratic field.",

author = "Masanori Morishita",

note = "Funding Information: Acknowledgement. I would like to thank M. Kapranov for suggesting an application of my Milnor invariants to the 2-class groups of quadratic fields. This work is partly supported by the Grants-in-Aid for Scientific Research, Ministry of Education, Culture, Sports, Science and Technology, Japan. Publisher Copyright: {\textcopyright} 2007 Birkh{\"a}user Verlag Basel/Switzerland.",

year = "2008",

doi = "10.1007/978-3-7643-8608-5_16",

language = "English",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "669--683",

booktitle = "Progress in Mathematics",

}