On pro-𝑝 link groups of number fields

Abstract

As an analogue of a link group, we consider the Galois group of the maximal pro- p p -extension of a number field with restricted ramification which is cyclotomically ramified at p p , i.e., tamely ramified over the intermediate cyclotomic Z p \mathbb Z_p -extension of the number field. In some basic cases, such a pro- p p Galois group also has a Koch type presentation described by linking numbers and mod 2 2 Milnor numbers (Rédei symbols) of primes. Then the pro- 2 2 Fox derivative yields a calculation of Iwasawa polynomials analogous to Alexander polynomials.