Tate sequences and lower bounds for ranks of class groups

Cornelius Greither. "Tate sequences and lower bounds for ranks of class groups." Acta Arithmetica 160.1 (2013): 55-66. <http://eudml.org/doc/279342>.

@article{CorneliusGreither2013,
abstract = {Tate sequences play a major role in modern algebraic number theory. The extension class of a Tate sequence is a very subtle invariant which comes from class field theory and is hard to grasp. In this short paper we demonstrate that one can extract information from a Tate sequence without knowing the extension class in two particular situations. For certain totally real fields K we will find lower bounds for the rank of the ℓ-part of the class group Cl(K), and for certain CM fields we will find lower bounds for the minus part of the ℓ-part of the class group. These results reprove and partly generalise earlier results by Cornell and Rosen, and by R. Kučera and the author. The methods are purely algebraic, involving a little cohomology.},
author = {Cornelius Greither},
journal = {Acta Arithmetica},
keywords = {Tate sequences; class groups; cohomology; totally real fields; CM fields},
language = {eng},
number = {1},
pages = {55-66},
title = {Tate sequences and lower bounds for ranks of class groups},
url = {http://eudml.org/doc/279342},
volume = {160},
year = {2013},
}

TY - JOUR
AU - Cornelius Greither
TI - Tate sequences and lower bounds for ranks of class groups
JO - Acta Arithmetica
PY - 2013
VL - 160
IS - 1
SP - 55
EP - 66
AB - Tate sequences play a major role in modern algebraic number theory. The extension class of a Tate sequence is a very subtle invariant which comes from class field theory and is hard to grasp. In this short paper we demonstrate that one can extract information from a Tate sequence without knowing the extension class in two particular situations. For certain totally real fields K we will find lower bounds for the rank of the ℓ-part of the class group Cl(K), and for certain CM fields we will find lower bounds for the minus part of the ℓ-part of the class group. These results reprove and partly generalise earlier results by Cornell and Rosen, and by R. Kučera and the author. The methods are purely algebraic, involving a little cohomology.
LA - eng
KW - Tate sequences; class groups; cohomology; totally real fields; CM fields
UR - http://eudml.org/doc/279342
ER -