Chern character and obstructions to deforming cycles

TL;DR

This paper uses the Chern character from K-theory to negative cyclic homology to address and eliminate obstructions in deforming algebraic cycles, advancing the understanding of cycle deformation theory.

Contribution

It introduces a novel approach leveraging the Chern character to remove obstructions in the deformation of algebraic cycles, building on recent work in the field.

Findings

Demonstrates how to eliminate obstructions to cycle deformation

Connects K-theory and negative cyclic homology via the Chern character

Provides a method to facilitate deformation of algebraic cycles

Abstract

Following Bloch-Esnault-Kerz and Green-Griffiths' recent works on deformation of algebraic cycle classes, we use Chern character from K-theory to negative cyclic homology to show how to eliminate obstructions to deforming cycles.