TL;DR
This paper introduces toy shtukas, a simplified model inspired by Drinfeld shtukas, and studies their moduli scheme, revealing properties of horospherical divisors and a canonical morphism linking to Drinfeld shtukas.
Contribution
It defines toy shtukas and analyzes their moduli scheme, establishing properties of horospherical divisors and describing the pullback from Drinfeld shtukas.
Findings
Basic properties of the moduli scheme of toy shtukas are established.
A description of the space of principal toy horospherical divisors is provided.
A canonical morphism from Drinfeld shtukas to toy shtukas moduli scheme is constructed.
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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology · Mathematics and Applications