The integral Chow ring of $\overline{\mathcal{M}}_{1,3}$

TL;DR

This paper computes the integral Chow ring of the moduli space of stable elliptic curves with three marked points using advanced patching techniques and higher Chow groups with -adic coefficients.

Contribution

It provides the first explicit computation of the integral Chow ring for ,3, introducing novel methods that combine patching techniques and higher Chow groups.

Findings

Explicit description of the integral Chow ring of ,3

Development of new patching techniques for Chow ring computations

Application of higher Chow groups with -adic coefficients

Abstract

In this paper we compute the integral Chow ring of the moduli space of stable elliptic curves with three marked points by combining several patching techniques, including higher Chow groups with $\ell$-adic coefficients.