Outputs (4)

Further counterexamples to a conjecture of Beilinson (2008)
Journal Article
de Jeu, R. (2008). Further counterexamples to a conjecture of Beilinson. K-Theory, 1(1), 169-173. https://doi.org/10.1017/is007011012jkt001

We give stronger counterexamples to a conjecture of Beilinson.

Numerical verification of Beilinson's conjecture for K_2 of hyperelliptic curves (2006)
Journal Article
Dokchitser, T., de Jeu, R., & Zagier, D. (2006). Numerical verification of Beilinson's conjecture for K_2 of hyperelliptic curves. Compositio Mathematica, 142(2), 339-373. https://doi.org/10.1112/s0010437x05001892

We construct families of hyperelliptic curves over 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... Read More about Numerical verification of Beilinson's conjecture for K_2 of hyperelliptic curves.

The syntomic regulator for the K-theory of fields (2003)
Journal Article
Besser, A., & de Jeu, R. (2003). The syntomic regulator for the K-theory of fields. Annales Scientifiques de l’École Normale Supérieure, 36(6), 867-924. https://doi.org/10.1016/j.ansens.2003.01.003

We define complexes analogous to Goncharov's complexes for the K-theory of discrete valuation rings of characteristic zero. Under suitable assumptions in K-theory, there is a map from the cohomology of those complexes to the K-theory of the ring unde... Read More about The syntomic regulator for the K-theory of fields.

A remark on the rank conjecture (2002)
Journal Article
de Jeu, R. (2002). A remark on the rank conjecture. K-Theory, 25(3), 215-231. https://doi.org/10.1023/a%3A1015656301533

We prove a result about the action of -operations on the homology of linear groups. We use this to give a sharper formulation of the rank conjecture as well as some shorter proofs of various known results. We formulate a conjecture about how the shar... Read More about A remark on the rank conjecture.