Communications in Number Theory and Physics

Volume 13 (2019)

Number 2

Specialization of cycles and the $K$-theory elevator

Pages: 299 – 349



P. Luis del Ángel R (Centro de Investigación en Matemáticas, Guanajuato, Gto., México)

C. Doran (Department of Mathematics, University of Alberta, Edmonton, Alb., Canada)

M. Kerr (Department of Mathematics, Washington University, St. Louis, Missouri, U.S.A.)

J. Lewis (Department of Mathematics, University of Alberta, Edmonton, Alb., Canada)

J. Iyer (Institute of Mathematical Sciences, Chennai, India)

S. Müller-Stach (Institut für Mathematik, Johannes Gutenberg Universität, Mainz, Germany)

D. Patel (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)


A general specialization map is constructed for higher Chow groups and used to prove a “going-up” theorem for algebraic cycles and their regulators. The results are applied to study the degeneration of the modified diagonal cycle of Gross and Schoen, and of the coordinate symbol on a genus-$2$ curve.

2010 Mathematics Subject Classification

Primary 14C25, 19E15. Secondary 14C30.

The authors acknowledge partial support under NSF FRG grant DMS-1361147 (Kerr), NSF grant DMS-1502296 (Patel), grants from the Natural Sciences and Engineering Research Council of Canada (Doran, Lewis), and DFG grant SFB/TRR 45 (Müller-Stach).

Received 18 April 2017

Accepted 8 December 2018

Published 26 April 2019