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International conference ''Algebra, algebraic geometry and number theory'' dedicated to the memory of academician Igor Rostislavovich Shafarevich
June 13, 2018 11:20–12:20, Moscow, Steklov Mathematical Institute of RAS, 8, Gubkina str., Conference hall
 


Galois groups of $p$-extensions of higher local fields

V. A. Abrashkin
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MP4 839.2 Mb

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V. A. Abrashkin


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Abstract: Suppose $K$ is a finite extension of the field of $p$-adic numbers containing a primitive $p$-th root of unity. Then the Galois group $G(p)$ of the maximal $p$-extension of $K$ has finitely many generators and one (Demushkin) relation of very special form. In the talk we will discuss the structure of the maximal quotient of $G(p)$ of period $p$ and nilpotent class $<p$ in the case of local fields $K$ of dimension $>1$.

Language: English

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