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arXiv · 1604.08049

Higher-dimensional Contou-Carr\`ere symbol and continuous automorphisms

Sergey Gorchinskiy·Denis Osipov
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Abstract

We prove that the higher-dimensional Contou-Carr\`ere symbol is invariant under continuous automorphisms of algebras of iterated Laurent series over a ring. Applying this property, we obtain a new explicit formula for the higher-dimensional Contou-Carr\`ere symbol. Unlike previously known formulas, this formula is given over an arbitrary ring, not necessarily a $\mathbb Q$-algebra, and does not involve algebraic $K$-theory.

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Sergey Gorchinskiy, Denis Osipov. 2016-04-27. Higher-dimensional Contou-Carr\`ere symbol and continuous automorphisms. https://doi.org/10.1007/s10688-016-0158-8

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