On Gras conjecture for imaginary quadratic fields

TL;DR

This paper extends Rubin's methods to prove the Gras conjecture for abelian extensions of imaginary quadratic fields, specifically addressing primes dividing roots of unity, advancing understanding in algebraic number theory.

Contribution

It introduces new techniques to prove the Gras conjecture for specific cases involving imaginary quadratic fields and primes dividing roots of unity.

Findings

Proved the Gras conjecture for certain abelian extensions of imaginary quadratic fields.

Extended Rubin's methods to new cases involving primes dividing roots of unity.

Enhanced understanding of class group structures in these fields.

Abstract

In this paper we extend methods of Rubin to prove the Gras conjecture for abelian extensions of a given imaginary quadratic field k and prime numbers p which divide the number of roots of unity in k.