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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 241, Pages 8–42
(Mi tm386)
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This article is cited in 6 scientific papers (total in 6 papers)
An Analogue of the Grothendieck Conjecture for Two-Dimensional Local Fields of Finite Characteristic
V. A. Abrashkinab a Steklov Mathematical Institute, Russian Academy of Sciences
b University of Durham
Abstract:
In the case of a local field $K$ of finite characteristic $p>0$, a local analogue of the Grothendieck conjecture appears as a characterization of “analytic” automorphisms of the Galois group $\Gamma _K$ of $K$, i.e. the automorphisms of the topological group $\Gamma _K$ induced by conjugation by the automorphisms of the algebraic closure $\overline K$ of $K$ that leave the field $K$ invariant. Earlier, it was proved by the author that necessary and sufficient conditions for such a characterization in the case of one-dimensional local fields $K$ of characteristic $p\geq 3$ are the compatibility of these fields with the ramification filtration of the Galois group $\Gamma _K$. In the present paper, it is shown that, in the case of multidimensional local fields, the compatibility with the ramification filtration supplemented with certain natural topological conditions is still sufficient for the characterization of analytic automorphisms of $\Gamma _K$.
Received in December 2002
Citation:
V. A. Abrashkin, “An Analogue of the Grothendieck Conjecture for Two-Dimensional Local Fields of Finite Characteristic”, Number theory, algebra, and algebraic geometry, Collected papers. Dedicated to the 80th birthday of academician Igor' Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 241, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 8–42; Proc. Steklov Inst. Math., 241 (2003), 2–34
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https://www.mathnet.ru/eng/tm386 https://www.mathnet.ru/eng/tm/v241/p8
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Abstract page: | 309 | Full-text PDF : | 84 | References: | 59 |
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