The motivic fundamental group of a punctured elliptic curve and algebraic cycles

TL;DR

This paper studies the motivic fundamental group of punctured elliptic curves using DG complexes, providing a resolution via Schur complexes and identifying algebraic cycles similar to Bloch-Totaro cycles.

Contribution

It introduces a DG complex framework for the motivic fundamental group of punctured elliptic curves and describes its resolution with Schur complexes, along with new algebraic cycles.

Findings

Resolution of the motivic fundamental group via Schur complexes

Identification of algebraic cycles analogous to Bloch-Totaro cycles

Framework connecting elliptic motives and algebraic cycles

Abstract

In this paper, we consider the motivic fundamental group of the punctured elliptic curves as a DG complex in the DG category of elliptic motives and describe its resolution via Schur complexes. During this process, we find the algebraic cycles analogous to the Bloch-Totaro cycles.