Height Pairing on Higher Cycles and Mixed Hodge Structures II

TL;DR

This paper introduces new height invariants for higher algebraic cycles using mixed Hodge structures, generalizing classical height concepts and establishing their key properties.

Contribution

It constructs two new height functions for Bloch higher cycles via mixed Hodge structures, extending classical height theories to higher cycles.

Findings

Defined two height invariants for higher cycles

Proved key properties of these height functions

Generalized classical biextension height to higher cycles

Abstract

We attach a mixed Hodge structure and associate two versions of heights to a pair of Bloch higher cycles. Both these heights generalize the biextension height attached to a pair of classical algebraic cycles homologous to zero. We also prove several salient properties of these heights.