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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)].

Bounds For Étale Capitulation Kernels II

Mohsen Asghari-Larimi, Abbas Movahhedi (2009)

Annales mathématiques Blaise Pascal

Let p be an odd prime and E / F a cyclic p -extension of number fields. We give a lower bound for the order of the kernel and cokernel of the natural extension map between the even étale K -groups of the ring of S -integers of E / F , where S is a finite set of primes containing those which are p -adic.

Capitulation for even K -groups in the cyclotomic p -extension.

Romain Validire (2009)

Journal de Théorie des Nombres de Bordeaux

Let p be a prime number and F be a number field. Since Iwasawa’s works, the behaviour of the p -part of the ideal class group in the p -extensions of F has been well understood. Moreover, M. Grandet and J.-F. Jaulent gave a precise result about its abelian p -group structure.On the other hand, the ideal class group of a number field may be identified with the torsion part of the K 0 of its ring of integers. The even K -groups of rings of integers appear as higher versions of the class group. Many authors...

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