On the integral Chow rings of various moduli stacks of curves

Abstract

The contents of this thesis are focused on the intersection theory of the stack of marked(stable or smooth) elliptic curves. We first recount some results on equivariant intersection theory, then give an exposition of some known results for the $n=1,2$ cases. Along the way, we provide some original proofs of these results as well as compute the higher Chow groups with $\ell$-adic coefficients for many of these stacks. The primary results, the integral Chow rings of $\overline{\mathcal M_{1,n}}$ for $n=3,\dots,10$, are contained in the last chapter.