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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On pro-$ p$ link groups of number fields


Author: Yasushi Mizusawa
Journal: Trans. Amer. Math. Soc. 372 (2019), 7225-7254
MSC (2010): Primary 11R23; Secondary 11R18, 11R32, 57M05
DOI: https://doi.org/10.1090/tran/7787
Published electronically: February 6, 2019
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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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Additional Information

Yasushi Mizusawa
Affiliation: Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466-8555, Japan
Email: mizusawa.yasushi@nitech.ac.jp

DOI: https://doi.org/10.1090/tran/7787
Received by editor(s): July 11, 2018
Received by editor(s) in revised form: December 17, 2018
Published electronically: February 6, 2019
Additional Notes: This work was supported by JSPS KAKENHI Grant Numbers JP26800010, JP17K05167.
Article copyright: © Copyright 2019 American Mathematical Society