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Tate sequences and lower bounds for ranks of class groups

Cornelius Greither (2013)

Acta Arithmetica

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...

The $ℓ$ -rank of the real class group of cyclotomic fields

Gary Cornell, Michael I. Rosen (1984)

Compositio Mathematica

The period-index problem in WC-groups IV: a local transition theorem

Pete L. Clark (2010)

Journal de Théorie des Nombres de Bordeaux

Let $K$ be a complete discretely valued field with perfect residue field $k$ . Assuming upper bounds on the relation between period and index for WC-groups over $k$ , we deduce corresponding upper bounds on the relation between period and index for WC-groups over $K$ . Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of LLR models of torsors under abelian varieties with good reduction and...

The Quadratic Schur Subgroup over Local and Global Fields.

C. Riehm (1989)

Mathematische Annalen

The Schur Subgroup of a Real Cyclotomic Field.

Toshihiko Yamada (1974)

Mathematische Zeitschrift