Rob de Jeu

Numerical verification of Beilinson's conjecture for K 2 of hyperelliptic curves

We construct families of hyperelliptic curves over Q of arbitrary genus g with (at least) g integral elements in K2. We also verify the Beilinson conjectures about K2 numerically for several curves with g = 2, 3, 4 and 5. The first few sections of the paper also provide an elementary introduction to the Beilinson conjectures for K2 of curves.

Motives and Algebraic Cycles: A Celebration in Honour of Spencer J. Bloch

Spencer J. Bloch has, and continues to have, a profound influence on the subject of Algebraic

Li(p)-service? An algorithm for computing p-adic polylogarithms

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Towards Regulator Formulae for the K-Theory of Curves over Number Fields

-Theory, Cycles and Motives. This book, which is comprised of a number of independent research articles written by leading experts in the field, is dedicated in his honour, and gives a snapshot of the current and evolving nature of the subject. Some of the articles are written in an expository style, providing perspective on the current state of the subject to those wishing to learn more about it. Others are more technical, representing new developments and making them especially interesting to researchers for keeping abreast of recent progress.

Zagier’s conjecture and Wedge complexes in algebraic

We describe an algorithm for computing Colemans p-adic poly-logarithms up to a given precision.

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In this paper we study the group K2n(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 K2n(n+1)(F), using the complexes constructed in Compositio Math.96 (1995), pp. 197–247. We study the boundary map in the localization sequence for n=2 and n=3. We combine our results with 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) (which have the same images as K4(C)⊗Z Q, and K6(C)⊗ Z, Q, respectively), independent of any conjectures.In this paper we study the group K2n(n+1)(F) where F is the function field of a complete, smooth, geometrically irreducible curve C over a number field, assuming the Beilinson–Soule conjecture on weights. In particular, we compute the Beilinson regulator on a subgroup of K2n(n+1)(F), using the complexes constructed in Compositio Math.96 (1995), pp. 197–247. We study the boundary map in the localization sequence for n=2 and n=3. We combine our results with 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) (which have the same images as K4(C)⊗Z Q, and K6(C)⊗ Z, Q, respectively), independent of any conjectures.