In mathematics, the Contou-Carrère symbola,b〉 is a Steinberg symbol defined on pairs of invertible elements of the ring of Laurent power series over an Artinian ring k, taking values in the group of units of k. It was introduced by Contou-Carrère (1994).

Definition

If k is an Artinian local ring, then any invertible formal Laurent series a with coefficients in k can be written uniquely as

where w(a) is an integer, the elements ai are in k, and are in m if i is negative, and is a unit if i = 0.

The Contou-Carrère symbol 〈a,b〉 of a and b is defined to be

References

  • Contou-Carrère, Carlos (1994), "Jacobienne locale, groupe de bivecteurs de Witt universel, et symbole modéré", Comptes Rendus de l'Académie des Sciences, Série I (in French), 318 (8): 743–746, MR 1272340


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.