On -Ranks in the Class Field Tower Problem
Much recent progress in the 2-class field tower problem revolves around demonstrating infinite such towers for fields – in particular, quadratic fields – whose class groups have large 4-ranks. Generalizing to all primes, we use Golod-Safarevic-type inequalities to analyse the source of the -rank of the class group as a quantity of relevance in the -class field tower problem. We also make significant partial progress toward demonstrating that all real quadratic number fields whose class groups...