Equivariant Chow–Witt groups and moduli stacks of elliptic curves

Abstract

We introduce equivariant Chow–Witt groups in order to define Chow–Witt groups of quotient stacks. We compute the Chow–Witt ring of the moduli stack of stable (resp. smooth) elliptic curves, providing a geometric interpretation of the new generators. Along the way, we also determine the Chow–Witt ring of the classifying stack of ${\mu }_{2n}$.