Number Theory Seminar
The finitude of tamely ramified pro-p extensions of number fields with cyclic p-class groups
Speaker: Donghyeok Lim (Korea National University of Education)Date: Monday, 20 January 2025 - 14:00Place: Aula Naranja, ICMAT
Abstract:
For a given number field F and a finite set S of places of F, the S-ray p-class field tower problem asks whether the maximal pro-p extension of F, where only places in S are allowed to be ramified, is finite or not. It is a generalization of the p-Hilbert class field tower problem. While the Golod-Shafarevich test provides many examples of infinite towers, the finitude of such towers remains poorly understood, especially when the p-rank of the class group and the size of S is small. In this talk, we explain that if a number field F has a cyclic p-class group, then the {\mathfrak{q}}-ray p-class field tower of F is finite for the majority of primes \mathfrak{q} of F. This is a joint work with Yoonjin Lee.
