On the Steinberg property of the Contou-Carrere symbol

Abstract

The aim of this work is to show that the Contou-Carrère symbol satisfies the property of Steinberg symbols: $<f,1-f{>}_{A((t){)}^{\times }}=1$ for all elements $f,1-f\in A((t){)}^{\times }$. Moreover, we offer a cohomological characterization of the Contou-Carrère symbol from the commutator of a central extension of groups.

9 pages; a part on Witt parameters added; Lemma 3.2 modified

Cited by in corpus (2)

• On the Contou-Carrere Symbol for Surfaces
• Contou-Carrere symbol via iterated integrals and its reciprocity law