A Toy Model of Shtukas

In this thesis, we introduce the notion of toy shtukas. The motivation comes from the question of constructing certain rational functions on the moduli stack of Drinfeld shtukas. These rational functions are somewhat similar to modular units, with their divisors supported on the horospherical locus. 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. The main result of this thesis is a description of the space of principal horospherical divisors obtained from the pullback.