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Blaise Pascal
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Christian Maire; Cam McLeman
On $p^2$-Ranks in the Class Field Tower Problem
($p^2$-rangs et $p$-tours de Hilbert)
Annales mathématiques Blaise Pascal, 21 no. 2 (2014), p. 57-68, doi: 10.5802/ambp.342
Article PDF | Reviews MR 3322615
Class. Math.: 11R29, 11R34, 11R37
Keywords: Hilbert class field towers

Résumé - Abstract

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 $p^2$-rank of the class group as a quantity of relevance in the $p$-class field tower problem. We also make significant partial progress toward demonstrating that all real quadratic number fields whose class groups have a 2-rank of 5 must have an infinite 2-class field tower.

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