The Lichtenbaum conjecture for abelian extension of imaginary quadratic fields

TL;DR

This paper proves a significant conjecture in number theory related to abelian extensions of imaginary quadratic fields, confirming it for most primes except a finite set of exceptions.

Contribution

It establishes the cohomological Lichtenbaum conjecture for abelian extensions of imaginary quadratic fields, advancing understanding in algebraic number theory.

Findings

Proves the conjecture up to a finite set of bad primes

Confirms the conjecture for a broad class of imaginary quadratic fields

Provides new insights into the structure of abelian extensions

Abstract

In this paper, we prove the cohomological Lichtenbaum conjecture of abelian extensions of imaginary quadratic fields up to a finite set of bad primes.