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Tate sequences and lower bounds for ranks of class groups

100%

Greither C.

Acta Arithmetica

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2013

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tom 160

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nr 1

55-66

EN

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.

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On normal integral bases in ray class fields over imaginary quadratic fields

100%

Greither C.

Acta Arithmetica

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1996-1997

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tom 78

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nr 4

315-329

3

On totally real Hilbert-Speiser fields of type Cₚ

63%

Greither C., Johnston H.

Acta Arithmetica

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2009

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tom 138

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nr 4

329-336

4

Racines d'unités cyclotomiques et divisibilité du nombre de classes d'un corps abélien réel

51%

Greither C., Hachami S., Kučera R.

Acta Arithmetica

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2000-2001

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tom 96

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nr 3

247-259

Ograniczanie wyników

4 Acta Arithmetica

4 Greither C.

1 Hachami S.

1 Johnston H.

1 Kučera R.

1 2013

1 2009

1 2001

1 1997

Tate sequences and lower bounds for ranks of class groups

On normal integral bases in ray class fields over imaginary quadratic fields

On totally real Hilbert-Speiser fields of type Cₚ

Racines d'unités cyclotomiques et divisibilité du nombre de classes d'un corps abélien réel