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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)].

A really elementary proof of real Lüroth's theorem.

T. Recio, J. R. Sendra (1997)

Revista Matemática de la Universidad Complutense de Madrid

Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K is a subfield...

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