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Ramification theory for higher dimensional local fields

Abrashkin, Victor

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Authors

Victor Abrashkin



Abstract

The paper contains a construction of ramification theory for higher dimensional local fields $K$ provided with additional structure given by an increasing sequence of their "subfields of i-dimensional constants", where $0\le i\le n$ and $n$ is the dimension of $K$. It is also announced that a local analogue of the grothendieck Conjecture still holds: all automorphisms of the absolute Galois group of $K$, which are compatible with ramification filtration and satisfy some natural topological conditions appear as conjugations via some automorphisms of the algebraic closure of $K$.

Citation

Abrashkin, V. (2002). Ramification theory for higher dimensional local fields

Journal Article Type Article
Publication Date 2002
Deposit Date May 28, 2008
Publicly Available Date Mar 29, 2024
Journal Contemporary mathematics.
Peer Reviewed Peer Reviewed
Volume 300
Pages 1-16
Keywords Local fields, Ramification, Anabelian conjecture.
Publisher URL http://www.ams.org/bookstore?fn=20&arg1=conmseries&item=CONM-300

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Copyright Statement
First published in Contemporary mathematics in volume 300, 2002, published by the American Mathematical Society.




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