×

Numerical verification of Beilinson’s conjecture for \(K_2\) of hyperelliptic curves. (English) Zbl 1186.11037

Summary: We construct families of hyperelliptic curves over \(\mathbb Q\) of arbitrary genus \(g\) with (at least) \(g\) integral elements in \(K_2\). We also verify the Beilinson conjectures about \(K_2\) 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 \(K_2\) of curves.

MSC:

11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
19F27 Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects)
11G55 Polylogarithms and relations with \(K\)-theory
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
PDFBibTeX XMLCite
Full Text: DOI arXiv