Specialization of cycles and the K-theory elevator

TL;DR

This paper develops a specialization map for higher Chow groups, proving a 'going-up' theorem for algebraic cycles and regulators, with applications to cycle degeneration and coordinate symbols on genus-2 curves.

Contribution

It introduces a general specialization map for higher Chow groups and establishes a new 'going-up' theorem for algebraic cycles and regulators.

Findings

Proved a 'going-up' theorem for algebraic cycles and regulators.

Applied results to degeneration of the modified diagonal cycle.

Analyzed the coordinate symbol on a genus-2 curve.

Abstract

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.