Conformal blocks for modular vertex algebras

Abstract

Given a vertex operator algebra $V$ over $\mathbb{C}$, it is known how to define so-called sheaves of coinvariants and conformal blocks on the moduli space $\overline{\mathcal{M}}_{g,n}$ of stable, $n$-pointed, genus $g$ curves. We extend this theory to vertex algebras equipped with a notion of change of coordinates over any algebraically closed field. As a by-product of our arguments, we also show that a number of standard assumptions in these constructions can be removed, such as being $C_1$-cofinite or CFT-type.