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 | |
| Publication status | Published - Jan 1 2008 |
Publication series
| Name | Progress in Mathematics |
|---|---|
| Volume | 265 |
| ISSN (Print) | 0743-1643 |
| ISSN (Electronic) | 2296-505X |
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All Science Journal Classification (ASJC) codes
- Analysis
- Algebra and Number Theory
- Geometry and Topology
Cite this
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 proceeding › Chapter
}
TY - CHAP
T1 - Milnor invariants and l-class groups
AU - Morishita, Masanori
PY - 2008/1/1
Y1 - 2008/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85042855029&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042855029&partnerID=8YFLogxK
U2 - 10.1007/978-3-7643-8608-5_16
DO - 10.1007/978-3-7643-8608-5_16
M3 - Chapter
AN - SCOPUS:85042855029
T3 - Progress in Mathematics
SP - 669
EP - 683
BT - Progress in Mathematics
PB - Springer Basel
ER -