The Golod–Shafarevich inequality and the class field tower problem

Authors

  • Jordi Vilà Casadevall École Polytechnique Fédérale de Lausanne (EPFL)

DOI:

https://doi.org/10.2436/20.2002.02.33

Keywords:

number theory, class field tower problem, pro-p groups, Golod–Shafarevich inequality

Abstract

In this article we present a proof of the class field tower problem. We begin by introducing pro-p groups, explain how to describe them in terms of generators and relations, and present the Golod–Shafarevich inequality, which establishes a criterion for a pro-p group to be infinite. After introducing some notions from algebraic number theory, we apply the Golod–Shafarevich inequality to the class field tower problem. We obtain a criterion for a number field to have an infinite class field tower, and give explicit examples of number fields satisfying this criterion.

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Published

2024-01-26

How to Cite

Vilà Casadevall, J. (2024). The Golod–Shafarevich inequality and the class field tower problem. Reports@SCM, 8(1), 1–10. https://doi.org/10.2436/20.2002.02.33

Issue

Vol. 8 No. 1 (2023)

Section

Articles

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