Notes on the biextension of Chow groups

TL;DR

This paper explores four different methods to construct the biextension of Chow groups, demonstrating their equivalence, and introduces a new approach to Chow categories along with an explicit Weil pairing formula.

Contribution

It provides a comprehensive comparison of four existing constructions and introduces a novel approach to Chow categories with an explicit Weil pairing formula.

Findings

Demonstrates equivalence of four biextension constructions.

Introduces a new approach to Chow categories.

Provides an explicit formula for the Weil pairing.

Abstract

The paper discusses four approaches to the biextension of Chow groups and their equivalences. These are the following: an explicit construction given by S.Bloch, a construction in terms of the Poincare biextension of dual intermediate Jacobians, a construction in terms of K-cohomology, and a construction in terms of determinant of cohomology of coherent sheaves. A new approach to J.Franke's Chow categories is given. An explicit formula for the Weil pairing of algebraic cycles is obtained.