Determinant functors and deformation of Chow groups

TL;DR

This paper introduces a determinant functor-based approach to relate local Hilbert functors with K-theoretic cycle groups, providing new insights into the infinitesimal deformation of Chow groups of divisors.

Contribution

It establishes a natural transformation connecting Hilbert functors to K-theoretic cycle groups, addressing Bloch's question on infinitesimal Chow group deformation.

Findings

Established a natural transformation from local Hilbert functor to K-theoretic cycle groups.

Provided an answer to Bloch's question on infinitesimal deformation of Chow groups.

Extended the understanding of deformation theory in algebraic geometry.

Abstract

Using determinant functor, we describe a natural transformation from local Hilbert functor to K-theoretic cycle groups of codimension one, which were variants of Balmer's tensor triangular Chow groups. This enables us to answers a question of Bloch on infinitesimal deformation of Chow groups of divisors.