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A note on 2-dimensional arithmetic symbols on Gl(n, ΣS).

Fernando Pablos Romo (2007)

Publicacions Matemàtiques

The aim of this note is to offer a summary of the definitions and properties of arithmetic symbols on the linear group Gl(n, F) -F being an arbitrary discrete valuation field- and to show that the natural generalizations of the Parshin symbol on an algebraic surface S to the linear group Gl(n, ΣS) do not allow us to define new 2-dimensional symbols on S.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].

On the cyclotomic elements in K₂ of a rational function field

Kejian Xu, Chaochao Sun, Shanjie Chi (2014)

Acta Arithmetica

If l is a prime number, the cyclotomic elements in the l-torsion of K₂(k(x)), where k(x) is the rational function field over k, are investigated. As a consequence, a conjecture of Browkin is partially confirmed.

On the structure of Milnor K -groups of certain complete discrete valuation fields

Masato Kurihara (2004)

Journal de Théorie des Nombres de Bordeaux

For a typical example of a complete discrete valuation field K of type II in the sense of [12], we determine the graded quotients gr i K 2 ( K ) for all i > 0 . In the Appendix, we describe the Milnor K -groups of a certain local ring by using differential modules, which are related to the theory of syntomic cohomology.

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