Abstract
For an odd prime p, let K/k be a Galois p-extension and S be a set of primes of k containing the primes lying over p. For the prth roots μpr(K) of unity in K, we describe the so-called Sha group ShaS(G(K/k), μpr(K)) in terms of the Galois groups of certain subfields of K corresponding to S. As an application, we investigate a tower of extension fields kTii≥0 where kTi+1 is defined as the fixed field of a free part of the Galois group of the Bertrandias and Payan extension of kTi over kTi. This is called a tower of torsion parts of the Bertrandias and Payan extensions over k. We find a relation between the degrees {[kTi+1:kTi]}i≥0 over the towers. Using this formula we investigate whether the towers are stationary or not.
| Original language | English |
|---|---|
| Pages (from-to) | 563-583 |
| Number of pages | 21 |
| Journal | Israel Journal of Mathematics |
| Volume | 221 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2017 Sep 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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On the towers of torsion Bertrandias and Payan modules. / Seo, Soogil.
In: Israel Journal of Mathematics, Vol. 221, No. 2, 01.09.2017, p. 563-583.Research output: Contribution to journal › Article
TY - JOUR
T1 - On the towers of torsion Bertrandias and Payan modules
AU - Seo, Soogil
PY - 2017/9/1
Y1 - 2017/9/1
N2 - For an odd prime p, let K/k be a Galois p-extension and S be a set of primes of k containing the primes lying over p. For the prth roots μpr(K) of unity in K, we describe the so-called Sha group ShaS(G(K/k), μpr(K)) in terms of the Galois groups of certain subfields of K corresponding to S. As an application, we investigate a tower of extension fields kTii≥0 where kTi+1 is defined as the fixed field of a free part of the Galois group of the Bertrandias and Payan extension of kTi over kTi. This is called a tower of torsion parts of the Bertrandias and Payan extensions over k. We find a relation between the degrees {[kTi+1:kTi]}i≥0 over the towers. Using this formula we investigate whether the towers are stationary or not.
AB - For an odd prime p, let K/k be a Galois p-extension and S be a set of primes of k containing the primes lying over p. For the prth roots μpr(K) of unity in K, we describe the so-called Sha group ShaS(G(K/k), μpr(K)) in terms of the Galois groups of certain subfields of K corresponding to S. As an application, we investigate a tower of extension fields kTii≥0 where kTi+1 is defined as the fixed field of a free part of the Galois group of the Bertrandias and Payan extension of kTi over kTi. This is called a tower of torsion parts of the Bertrandias and Payan extensions over k. We find a relation between the degrees {[kTi+1:kTi]}i≥0 over the towers. Using this formula we investigate whether the towers are stationary or not.
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U2 - 10.1007/s11856-017-1556-1
DO - 10.1007/s11856-017-1556-1
M3 - Article
VL - 221
SP - 563
EP - 583
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
SN - 0021-2172
IS - 2
ER -