Towards regulator formulae for curves over number fields

1998/11/05 by Rob de Jeu, de Jeu, Rob
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/9811192

arxiv created 1998/11/05 · arxiv updated 2009/12/01

Abstract

In this paper we study the group K_2n⁽ⁿ⁺¹⁾(F) where F is the function field of a complete, smooth, geometrically irreducible curve C over a number field, assuming the Beilinson--Soulé conjecture on weights. In particular, we compute the Beilinson regulator on a subgroup of K_2n⁽ⁿ⁺¹⁾(F), using the complexes constructed in previous work by the author. We study the boundary map in the localization sequence for n = 3 (the case n = 2 was done in a previous paper). We combine our results with some results of Goncharov in order to obtain a complete description of the image of the regulator map on K₄⁽³⁾(C) and K₆⁽⁴⁾(C), independent of any conjectures.

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