Higher-dimensional Contou-Carrère symbol and continuous automorphisms

Abstract

We prove that the higher-dimensional Contou-Carrère 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-Carrère 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.

18 pages; minor changes

Cited by in corpus (5)

• Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds
• Formal Bott-Thurston cocycle and part of a formal Riemann-Roch theorem
• Relative Milnor $K$-groups and differential forms of split nilpotent extensions
• Witt vectors, commutative and non-commutative
• Local analog of the Deligne-Riemann-Roch isomorphism for line bundles in relative dimension $1$