Communications in Number Theory and Physics
Volume 13 (2019)
Specialization of cycles and the $K$-theory elevator
Pages: 299 – 349
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