A toy model of shtukas

Abstract

Motivated by the question of constructing certain rational functions (modular units) on the moduli stack of Drinfeld shtukas, we introduce the notion of toy shtukas. We prove basic properties of the moduli scheme of toy shtukas. Analogously to horospherical divisors on the moduli stack of Drinfeld shtukas, there are toy horospherical divisors on the moduli scheme of toy shtukas. We describe the space of principal toy horospherical divisors. There is a canonical morphism from the moduli stack of Drinfeld shtukas to the moduli scheme of toy shtukas. Our main result is a description of the space of principal horospherical divisors obtained from the pullback.