Construction of certain rational functions on the moduli stack of Drinfeld shtukas

TL;DR

This paper constructs specific rational functions on the moduli stack of Drinfeld shtukas, using a vanishing theorem and deformation theory to analyze their divisors supported on horospherical divisors.

Contribution

It introduces a novel method to construct rational functions on the moduli stack of Drinfeld shtukas and computes their divisors using a new vanishing theorem.

Findings

Rational functions (modular units) are constructed on the moduli stack.

Divisors of these functions are supported on horospherical divisors.

A vanishing theorem for shtukas is established and used in divisor calculation.

Abstract

We construct certain rational functions (modular units) on the moduli stack of Drinfeld shtukas. The divisors of these rational functions are supported on horospherical divisors of the moduli stack. The key to our construction is a vanishing theorem for shtukas with zeros and poles satisfying certain conditions. Using deformation theory, we calculate the divisors of these rational functions.