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arXiv · 1707.00113

On pro-$p$ link groups of number fields

Yasushi Mizusawa
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Abstract

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

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Yasushi Mizusawa. 2018-12-23. On pro-$p$ link groups of number fields. https://doi.org/10.1090/tran%2F7787

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