Tate sequences and lower bounds for ranks of class groups

• Autorzy: Cornelius Greither
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 160
• Numer: 1
• Strony: 55-66

Daty

wydano

2013

Twórcy

autor

Cornelius Greither

• Fakultät Informatik, Universität der Bundeswehr München, 85577 Neubiberg, Germany

Identyfikatory

DOI

10.4064/aa160-1-4